The solo shot also came on the Yankees' first at-bat of the 3-0 victory.
Tulowitzki -- who signed with the Yankees in January after being cut by the Blue Jays -- stepped up to face Toronto star Marcus Stroman as the team's leadoff hitter. Stroman began the exchange by earning a called strike on his former teammate.
Tulowitzki sent his next offering over the right field fence for a 1-0 lead.
The Yankees added another run on a Kyle Higashioka leadoff solo shot in the bottom of the second frame. Jorge Saez plated Ryan McBroom on a ground out in the bottom of the sixth inning for the final run of the game.
Tulowitzki went 1-for-2 with an RBI and run scored in the win. The 13-year veteran did not play last season due to foot injuries. The five-time All-Star hit .254 with 24 home runs and 79 RBIs in his last full season in 2016 for Toronto.
The Yankees host the Philadelphia Phillies in another spring training clash at 1:05 p.m. Tuesday in Tampa.