Junqueira started racing karts in Brazil and dominated Formula Three Sudamericana before moving to Formula 3000. He tested for the Williams Formula One team for many years, and came close to landing a race drive in 2000, losing out to Jenson Button. He rebounded from this setback, winning that year’s International Formula 3000 Championship.

In 2001 Junqueira joined the CART Championship Car series driving for Chip Ganassi Racing where he had immediate success, capturing a win in his 14th race and finished second in points with two wins the following year. In 2003 Ganassi left to the rival Indy Racing League and Junqueira joined Newman/Haas Racing, the top team remaining in what was now the Champ Car World Series. He captured series runner up honors in both 2003 and 2004, capturing two wins in each of those seasons. He also drove in the Indianapolis 500 four times for both Ganassi and Newman/Haas in one-off appearances. In 2002, he qualified for the pole position, and he twice finished 5th in the race.

In the 2005 Indianapolis 500 Junqueira crashed head-on into the turn one wall after colliding with backmarker A.J. Foyt IV. He suffered a concussion and a fractured vertebrae and missed the remainder of the 2005 Champ Car season. Junqueira was the Champ Car points leader at the time, having won the second race of the year in Monterrey, Mexico. Veteran Oriol Servia took his place and finished runner-up in the standings.

In 2006 he returned to the cockpit at Newman/Haas but for the first time in his career he did not win a race and only finished fifth in the championship while his teammate Sébastien Bourdais won his third straight title. He was replaced in the second Newman/Haas car in 2007 by rookie Graham Rahal and Junqueira signed to drive for Dale Coyne Racing as teammate to the inexperienced Katherine Legge. Junquiera finished seventh in the championship including three consecutive podium finishes late in the season.

In 2011, driving for A. J. Foyt, he qualified his car for the 500 in nineteenth position, only to once again have to give up his chance to drive in the actual race. Foyt sold the unsponsored car’s entry to Andretti Autosport, whose driver Ryan Hunter-Reay had been the final car bumped from the field. In 2012, he entered in for an injured Josef Newgarden at the first Grand Prix of Baltimore.