Nova (16-4) improved to 12-0 in his last 15 starts, baffling the Rays on six hits while walking three and striking out three for the American League East-leading Yankees.
Curtis Granderson smacked a bases-clearing double in the second inning and later added an RBI single, finishing 3-for-5 with four RBI for New York, which came into the contest with a five-game lead over second-place Boston.
Tampa Bay's Wade Davis (10-10) was roughed up for five runs on eight hits before exiting after 4 2/3 innings.
The Rays -- hoping to catch Boston for the AL wild card -- allowed the Red Sox to reduce their magic number to clinch the playoff spot to seven with nine contests remaining.
Tampa Bay came into the game trailing Boston by two games.