Harrison (17-9) has won nine consecutive starts against the Mariners, beating them four times this year alone. He allowed just six hits in Sunday's rubber match, one coming on Justin Smoak's homer in the eighth.
"He was outstanding," Rangers manager Ron Washington said of Harrison. "Everything we needed out of him today he gave to us."
Koji Uehara relieved Harrison with two on and two outs in the ninth and struck out Michael Saunders to earn his first save of the season.
Adrian Beltre broke a scoreless tie with his 33rd home run of the season in the fourth, and Mitch Moreland drove in the eventual game-winning run in the fifth to give the Rangers their fourth win in six games.
Coupled with Oakland's loss to the Orioles, the Rangers increased their lead in the AL West to three games over the Athletics.
Blake Beavan (9-10) was the hard-luck loser, allowing two runs on seven hits in seven innings of work.
An inning after Beltre cleared the left-field wall, Moreland doubled into the right-field corner to knock in David Murphy, who led off the frame with a single.
Other than Smoak's homer, Harrison did not allow a runner past first base until the ninth, when he walked Franklin Gutierrez with one away and gave up a two-out single to Jesus Montero.
"We took it all the way to the end...but they got the last out," Mariners manager Eric Wedge said.
Texas is 8-1-0 in its last nine series ... The longest win streak against one opponent in Rangers history belongs to Charlie Hough, who beat the Twins in 13 consecutive starts from 1984-88 ... Uehara's last save came on October 2, 2010 ... Michael Young had three of Texas' seven hits ... The game was delayed two hours, 12 minutes by rain and lasted two hours, 20 minutes.
09/16 22:37:11 ET