Teixeira's bases-loaded clout in the third inning -- his first of the season -- put the Yankees up 4-1, but the Indians battled back tie it in the fifth.
After Reid Brignac struck out, Austin Romine singled on a sharp grounder off Masterson, sending Sukuzi to third, then stole second.
Gardner followed by lining a pitch up the middle, easily scoring Suzuki. Romine also came around third and would have been nailed at the plate by center fielder Michael Bourn's throw, but Masterson cut it off, allowing a second run to score.
Masterson (8-4) was lit up for seven runs on nine hits over 6 1/3 innings.
Bourn stroked three hits and Mark Reynolds drove in a pair of runs for the Tribe.