Wilson (14-5) allowed just two hits and fanned six against four walks en route to his seventh consecutive positive decision dating back to a July 11 loss to Baltimore. Neftali Feliz posted a scoreless ninth to earn his 33rd save.
Bengie Molina and Elvis Andrus both collected two hits and drove in a run for the Rangers, who had dropped three of four coming in.
Billy Butler, Willie Bloomquist and Jai Miller notched the lone hits for the Royals, who have lost five of seven.
Kyle Davies (6-9) went 8 1/3 frames in the loss, as he yielded 10 hits and three runs — two earned — while fanning six.
Texas gave Wilson all the support he needed in the second, as Nelson Cruz doubled to start the frame, went to third on a David Murphy flyout and scored on a Molina base hit.
It was 2-0 for the Rangers in the fifth as Andres Blanco struck a leadoff triple and came in when Andrus followed with a single.
The visitors tacked on a run in the ninth, as Blanco singled with one down, moved to third on an Andrus hit and scored on Michael Young’s sacrifice fly.
Wilson avoided trouble in the second. After loading the bases with two down on two walks and a single, he fanned Miller looking. He also walked two in the sixth but was aided by a double play on a Jason Kendall grounder and a Wilson Betemit groundout.
Darren O’Day was called on with Miller on first and two outs to send down pinch-hitter Alex Gordon on a liner.
Feliz closed the door in the ninth, getting around a one-out single from Butler by inducing a game-ending double play grounder from Yuniesky Betancourt.
Texas has won six of seven from Kansas City in the season series, and has taken 16 of 22 since the start of the 2008 campaign…Prior to the game, the Rangers activated Cruz from the 15-day disabled list…To open a roster spot, the club optioned outfielder Brandon Boggs to Triple-A Oklahoma City…Texas also recalled outfielder Craig Gentry from Oklahoma City and placed him on the 15-day DL with a fractured right wrist suffered on August 13 while playing for the Triple-A affiliate.