Correia (9-10) notched his fourth straight start of allowing two or fewer earned runs, yielding one run on five hits. The right-hander issued one walk and struck out two.
Glen Perkins finished up with his 32nd save as the Twins took the rubber match of a three-game series.
Presley, obtained from the Pittsburgh Pirates Saturday in exchange for Justin Morneau, contributed a run-scoring single in his first game with his new team.
Rookie catcher Josmil Pinto went 2-for-4 with an RBI in his major-league debut and Doug Bernier also drove in a run for Minnesota.
Todd Blackley (2-2) absorbed the loss, yielding three runs on eight hits in 4 1/3 innings.
Mitch Moreland and A.J. Pierzynski each cracked a solo homer for American League West-leading Texas, which came into the contest with a two-game lead over second-place Oakland.
Notable deaths of 2014 [PHOTOS]