Texas starter Yu Darvish pitched seven shutout innings and left with a 1-0 lead.
The 20-year-old Profar connected off J.C. Gutierrez (0-1) for his second homer, a solo shot that put Texas ahead 2-1. David Murphy added an RBI single later in the inning.
Tanner Scheppers (4-0) got two outs in the eighth and Joe Nathan pitched a perfect ninth for his 17th save in 18 chances.
Darvish allowed three hits, walked two and struck out six. Alex Gordon doubled in the Kansas City eighth and scored on a grounder to make it 1-all.
The Rangers only had three singles coming into the eighth. A smiling Profar, called up from the minors on May 19, was enveloped by teammates when he ran into the dugout. Manager Ron Washington grabbed the rookie's batting helmet off his head.
Rangers center fielder Craig Gentry threw out Billy Butler at home trying to score early as first-place Texas won for the third time in four games.
The Rangers were without All-Star third baseman Adrian Beltre, who didn't play because of a strained left hamstring. Washington said Beltre may be back in the lineup for Tuesday night's game against the Boston Red Sox.
Kansas City starter Ervin Santana allowed an unearned run and three singles in seven innings. The right-hander had lost his last four starts coming in.
The Royals haven't scored more than four runs in a game since May 21 and have lost 10 of 12. Kansas City, which brought on Hall of Famer George Brett as interim hitting coach Thursday, scored only seven runs in dropping two of three to Texas.
Santana didn't allow a hit until Nelson Cruz singled with one out in the fourth.
Gordon, who snapped an 0-for-14 rut earlier in the game, led off the eighth with a broken-bat double against Neal Cotts. Alcides Escobar had a sacrifice bunt that moved Gordon to third.
Eric Hosmer hit a chopper to Jeff Baker, who played third base in place of Beltre. Baker's throw home was wild and Gordon scored easily to tie the game.
With the bases loaded and no outs in the second, Jeff Francoeur hit a liner to center and Gentry made a running catch. Gentry made a perfect throw to home plate and catcher Geovany Soto just got the tag on a sliding Butler.
NOTES: Rangers RHP Alexi Ogando will come off the disabled list and is scheduled to start Wednesday at Boston. Ogando (4-2) has been sidelined since May 16 with right biceps tendinitis. ... Kansas City OF David Lough did not play a day after getting hit on the right wrist by a pitch with the bases loaded in the 10th inning Saturday. X-rays on the wrist were negative. ... Brett and Rangers executive Nolan Ryan exchanged lineup cards before the game with umpire Dale Scott, who was behind home plate for the pair's final game on Oct. 3, 1993. Brett went 1 for 4 that day, Ryan was injured and didn't play.