Baker (5-4) won his third straight start, blanking the Padres on four hits while walking one and striking out 10. The right-hander lowered his ERA to 3.24 while throwing 80 of his 115 pitches for strikes as the Twins won their sixth straight.
Matt Capps turned in a 1-2-3 ninth for his 11th save, helping Minnesota to improve to 13-3 in June.
Valencia provided the game's only run with a solo homer to left in the second inning.
Tim Stauffer (2-5) absorbed the hard-luck loss for the Padres, yielding only the one run on six hits through seven innings. He didn't allow a walk while fanning five.
Light-hitting San Diego was shut out for the 12th time this season.
Notable deaths of 2014 [PHOTOS]