Tlustý began his North American hockey career when he was assigned to the Sault Ste. Marie Greyhounds of the Ontario Hockey League, holders of his OHL rights. In Tlustý's first 13 games of his OHL career, he sustained a serious high-ankle sprain that kept him out of the lineup for nearly 6 weeks as he attended treatment in Toronto. The injury also kept him from joining the Czech National team at the World Junior Hockey Championships, although he was named to the pre-tournament roster.
He made his return to the lineup in January 2007. He finished his first regular season in the OHL with 13 goals, 21 assists for 34 points in 37 games. With Tlustý back in the lineup, the Greyhounds made a strong finish leading into the playoffs and scored an upset in the first round, eliminating the Saginaw Spirit in 6 games. In the next round they faced the London Knights and lost in 7 games. Tlustý played well in the playoffs, scoring 9 goals and 8 assists for 17 points in 13 games.
Tlustý was drafted in the first round, 13th overall, in the 2006 NHL Entry Draft by the Toronto Maple Leafs. On July 14, 2006, Tlustý signed a three-year entry-level contract with the Maple Leafs, while appearing wearing #41 in training camp. On September 25, 2006, Tlustý was assigned to the Toronto Marlies of the American Hockey League where he began his professional career by scoring three goals and one assist in six games. On October 23, 2006, he was sent back to Sault Ste. Marie for more conditioning in junior hockey.
Tlustý attended the 2007 Toronto Maple Leafs prospect camp tournament for players who had been selected in the NHL Entry Draft, but had yet to play in the NHL. He played in all four games, three goals and adding an assist for a total of four points.
After the 2007 Prospects camp, Tlustý attended the Toronto Maple Leafs training camp and pre-season. He played four games in the pre-season and earned three assists. He qualified for final cuts before being sent down to the AHL again. He played in 5 games in the AHL, scoring one goal and two assists.
On October 25, 2007, Tlustý played his first regular season NHL game against the Pittsburgh Penguins, scoring two goals in his debut. His first goal was originally a shot by Alex Steen, but it deflected off of Tlustý's backside and went in the net. Thirty-five seconds later, he scored with a wrist shot from the wing. He earned his first assist on November 2. When he entered the NHL he was number 41, however, he later switched his number to 11. Tlustý played in 58 regular season games for the Maple Leafs in 2007-08, scoring 10 goals and adding 6 assists. He was expected to be a large part of the rebuilding Maple Leafs' offense in 2008-09. However, Tlusty struggled in the early part of the season, and was sent down to the Marlies. He has since been recalled due to roster shortages on the Leafs, but was demoted once again to clear room for Maple Leaf players returning from injury.