The family emigrated to Australia in 1949 and spent the first six months living at the Bonegilla Migrant Reception and Training Centre. According to Jesaulenko, the family name should have been spelt Esaulenko, but immigration officials actually listed “Esaulenko” with a “J” in front, thinking that they had heard a “J” in his name.

Jesaulenko moved to Melbourne in November 1966, and during his first pre-season was soon left in no doubt the standard that Barassi required at Carlton:

Jesaulenko first met Pratt when he arrived at Carlton in 1966, and remembered him fondly:

Jesaulenko made his senior VFL debut in the opening round of the 1967 season against Fitzroy at Princes Park, where he had 14 touches and kicked two goals in a 94-point victory. He would play every game for Carlton that season, one of four players to do so. In that season’s Brownlow Medal count, he would poll 15 votes to finish third behind eventual winner Ross Smith (24 votes) from St Kilda and North Melbourne’s Laurie Dwyer (17 votes). Jesaulenko would go on to play in four Carlton premierships – in 1968, 1970, 1972 and 1979. Jesaulenko was selected for All-Australian honours in 1969 and 1972. He also has the dubious record at Carlton for the most inaccurate score of 5 goals and 12 behinds, against Hawthorn in 1969.

A spectacular and popular player Jesaulenko was renowned for his high marking, mercurial ground play, superb balance and goal kicking. He kicked 115 goals in the 1970 season, breaking the club record and becoming the first (and, as of 2019, only) player to kick more than 100 goals in a season for Carlton. He went on to play in the famous 1970 VFL Grand Final against Collingwood. In front of an all-time record MCG crowd of 121,696 fans Carlton came from a 44-point deficit at half-time to win by 10 points.

Jesaulenko’s marking skill was perhaps best highlighted by a spectacular mark over big Collingwood ruckman Graeme Jenkin in the 1970 VFL Grand Final. The commentary has Mike Williamson shouting the now famous phrase “Oh Jesaulenko, you beauty!”. This “specky” is acclaimed by some to be the “Mark of the Century” and was the first to be recognised officially as the Mark of the Year; the medal awarded to the annual winner is called the Alex Jesaulenko Medal. Jesaulenko has downplayed the specky, citing other marks he took—even during the same game—as greater feats. He later said: “The images make it look classical, like it was taken from the marking manual, … It was against Collingwood, a Grand Final, the biggest crowd ever, Graeme’s a six-foot-four ruckman, I guess there’s a mystique in standing on top of him with your arms outstretched.” The mark is captured in Jamie Cooper’s painting The Game That Made Australia, commissioned by the AFL in 2008 to celebrate the 150th anniversary of the sport.

Jesaulenko had pay disputes with Carlton in 1977. Subsequently, he tied his ongoing presence at the club to then Carlton club president George Harris. At the end of the 1979 season, despite the premiership, Harris was ousted from his position and Jesaulenko cut all ties with Carlton.

Jesaulenko’s sparkling achievements were recognized not just in the football world; on 30 December 1978 he was made a Member (Civil) of the Order of the British Empire for service to the sport of Australian Rules football.

In 1979 Jesaulenko was the playing coach of Carlton’s premiership team, perhaps his finest moment in football. “Jezza” was, in fact the last playing coach in the VFL/AFL to win a premiership, and is likely to remain so indefinitely.

In a deal managed by trucking millionaire and St Kilda club president, Lindsay Fox, Jesaulenko moved to the St Kilda Football Club in 1980. While initially appointed as an on-field player only, Jesaulenko was then appointed playing coach when the incumbent St Kilda coach, Mike Patterson, was sacked by Fox after Round 2. He played 23 games and kicked 20 goals for the Saints in 1980–1981 and stayed on for a further season as coach. Jesaulenko retired as player after Round 8, 16 May 1981. He was the last person to serve as captain-coach in the VFL (Malcolm Blight was a playing coach until Round 16 of the same season, but was not captain during this time.)

Jesaulenko is mentioned in the 1985 song “The Back Upon Which Jezza Jumped” by Melbourne band TISM (This Is Serious Mum), appearing on the band’s self-title demo tape. The song depicts Graeme “Jerker” Jenkin being left to be forgotten because of Jezza’s spectacular mark.

When Carlton set up their Hall of Fame in 1987, Jesaulenko was one of the inaugural inductees. He was also an inaugural inductee into the Australian Football Hall of Fame in 1996, and in 2008 was elevated to Legend status. In 1996 he was also named on the half-forward flank in the AFL Team of the Century.

In the first half of the 1989 VFL season, Carlton was in disarray: Communication had almost completely broken down between the players and coach Robert Walls, who only two seasons ago had guided the Blues to the flag. Carlton had fallen one game short of the Grand Final in 1988, but started the 1989 season with five straight losses. The defining point came after losing to the Brisbane Bears by three points in Round 10 at home, with Warwick Capper kicking the winning goal after the siren. At that stage the Blues were second-last on the ladder with only two wins and in danger of “winning” their first-ever wooden spoon. Walls was sacked hours after the match. Jesaulenko had not been back at Carlton since his acrimonious departure almost a decade earlier, when he was appointed caretaker coach for the remainder of the season. Holding his first press conference after training at Princes Park for the upcoming match against Sydney, he seemed confident in restoring Carlton’s fortunes:

Jesaulenko’s optimism appeared to rub off on the Carlton players; they beat Sydney by 28 points and would win six more games to finish eighth. The Blues were expected to return to the top of the ladder in 1990, but won only fifty percent of their games and Jesaulenko was replaced by David Parkin. His last coaching appointment, at Coburg for the 1993 season, was a total disaster, with the Lions losing all eighteen games during a losing sequence of thirty games in the dying days of the Victorian Football Association.

In 1997 he was inducted as an official Legend of the Carlton Football Club. When the Carlton Team of the Century was announced, Jesaulenko was also named on the half-forward flank.

In 2002, he was inducted into the Ukrainian Sports Hall of Fame.

In 2006, Jesaulenko was featured in a Toyota Memorable Moments commercial with Stephen Curry and Dave Lawson, which involved spraypainting Jesaulenko’s navy suit and trying several methods to recreate the famous mark he took in the 1970 Grand Final, including a small trampoline, a stepladder and finally successfully with a large crane.

When it was known that Pratt was in his last days in April 2009, Jesaulenko contemplated paying him a farewell visit at his mansion, but thought better of it lest he attracted too much attention.

On 20 October 2010 he was inducted into the Sport Australia Hall of Fame.

In 2012, singer-songwriter Tex Perkins wrote and performed “Jesaulenko, You Beauty” exclusively for The Marngrook Footy Show.

In July 2013, Jesaulenko was named captain of the first Australia Post Multicultural Team of Champions.