Crosby's second NHL season also saw significant improvements for the Penguins franchise as a whole, as the emergence of Calder Trophy-winner Evgeni Malkin and runner-up Jordan Staal complemented the club's offence. As a result, the Penguins jumped from last place in the Eastern Conference the previous season to fifth for the club's first playoff appearance since 2001. Playing the Ottawa Senators in the opening round, Crosby scored a goal in his Stanley Cup playoff debut in a 6–3 loss. He finished the series with five points in five games as the Penguins were ousted by the eventual Stanley Cup runner-up. Following the Penguins defeat, Crosby was named Pittsburgh's team captain on May 31, 2007, making him (at 19 years, 9 months, and 24 days) the youngest team captain in NHL history. During the season, the Penguins had offered him the captaincy, but he had turned it down. In the press conference naming him the team captain, he explained:
At the NHL's annual awards show later in June 2007, Crosby completed a rare off-season "hat-trick", winning the Hart Memorial Trophy and the Lester B. Pearson Award in addition to his previously-clinched Art Ross Trophy. He became the youngest player in NHL history to win the Lester B. Pearson, and only the second youngest player ever to win the Hart (after Gretzky). He became the youngest player ever to be named to the NHL's First All-Star Team.
With Crosby's initial three-year, entry-level contract set to expire at the end of the following season, the Penguins signed him to a five-year, $43.5 million contract extension on July 10, 2007, ensuring his stay with the Penguins through the 2012–13 season. Midway through the subsequent season, Crosby recorded a Gordie Howe hat-trick on December 20, 2007, in a game against the Boston Bruins. His first assist came 55 seconds into the first period. At 8:26 of the same period, Crosby scored to give the Penguins a 2–0 lead. Then, five minutes and nine seconds into the second frame, Crosby fought ex-Penguin defenceman Andrew Ference to complete the hat-trick. This was Crosby's first NHL fight. In NHL's first Winter Classic (with a record crowd of 71,217 fans in attendance), Crosby scored the shootout winner in heavy snowfall to defeat the Buffalo Sabres. However, two weeks later, on January 18, 2008, Crosby suffered a high ankle sprain crashing leg-first into the boards in a game against the Tampa Bay Lightning. As a result, he missed the 2008 All-Star Game, to which he was named a starter. After missing 21 games, he returned on March 4 against the Lightning and earned an assist. However, two games after his return, he felt his ankle was not up to shape and decided that he needed more time for it to heal. Crosby consequently sat out of the Penguins' next seven games and returned on March 27, 2008, to help the Penguins defeat the New York Islanders 3–1. Despite his injury-shortened campaign, Crosby still managed 72 points in just 53 games.
In the 2009–10 NHL season, Crosby tied Tampa Bay Lightning centre Steven Stamkos for the lead in goals scored, with 51 goals, earning the Rocket Richard Trophy. He also garnered 58 assists for a total of 109 points, enough to tie with Alexander Ovechkin for second in league points, trailing only the Vancouver Canucks' Henrik Sedin's 112. Crosby was also named a finalist for the Hart Memorial Trophy and Ted Lindsay Award. Crosby won the Mark Messier Leadership Award, getting recognized as a "superior leader within the sport, setting a positive example through on-ice performance, motivation of team members and a dedication to the community". This was the second time he had received this honour, the other being in January 2007, during the award's first year when it was presented monthly. He was also included on NHL's all-decade second team of 2000s.