It was the first time the teams faced each other since the Panthers won 6-1 in Game 7 of the Eastern Conference Second Round on May 18.
Bobby McMann had two assists, and Joseph Woll made 26 saves for Toronto (12-11-3), which has won three of its past four.
Sam Reinhart scored, and Sergei Bobrovsky made 26 saves for Florida (12-12-1), which has lost three in a row and four of five.
Stecher gave the Maple Leafs a 1-0 lead at 5:24 of the first period, scoring with a point shot through traffic.
Joshua made it 2-0 at 7:54. He took a pass from McMann on the rush and shot over Bobrovsky’s right pad.
Reinhart, playing his 800th NHL game, cut it to 2-1 with a short-handed goal at 14:43 of the second period. After winning a puck battle in the left corner, Anton Lundell found Reinhart alone in the slot, where he waited out Woll and beat him over the glove.
Scott Laughton gave Toronto a 3-1 lead at 12:18 of the third period with his first goal of the season, scoring on a bouncing puck in front of the net.
John Tavares scored into an empty net at 19:41 for the 4-1 final.