Masterson (11-7) retired 17 of the first 18 batters he faced before allowing his first and only hit -- Brian Dozier's broken-bat double leading off the seventh.
The right-hander ended up yielding one run, didn't issue a walk and struck out eight, tossing 67-of-93 for strikes in the dominating performance.
Kipnis clouted a two-run shot in the third, giving the Indians a 3-0 lead, and later added a run-scoring single for three RBI.
Michael Brantley added a bases-clearing triple as the Tribe salvaged one win in a three-game series.
Cleveland remained 1 1/2 games behind American League Central-leading Detroit with the victory.
Twins starter Scott Diamond (5-9) was roughed up for six runs (five earned) on seven hits in a 4 2/3-inning effort.
Joe Mauer got the only RBI for Minnesota, which saw its four-game winning streak snapped.
2014: The Year in Music [PHOTOS]