The Rangers will now wait and see if their top two sluggers will be sidelined.
Hamilton and Beltre homered before each left the game with injuries, and Texas beat the slumping Cleveland Indians 5-2.
Hamilton left in the eighth with left knee soreness and Beltre exited in the fifth with a strained left shoulder. Beltre had an MRI on Wednesday night and the results won't be known until Thursday. Texas manager Ron Washington said taking Hamilton out of the game was precautionary and he didn't consider the injury serious.
"Hopefully, things won't last long with those guys," Washington said. "But we certainly can't stop the season, so we're going to play with what we've got and we're going to expect to win."
Beltre injured his shoulder when he made a diving stop of Russ Canzler's grounder in the second.
Mike Olt, who replaced Beltre at third, left the game in the bottom of the seventh with plantar fasciitis in his right foot. Olt, who will have an MRI Thursday, was limping just before he reached first beating out an infield single.
"Hopefully it's just precautionary," Kinsler said of his teammates' injuries.
Beltre hit a two-run homer in the first, his 13th in his last 20 games, and Hamilton added a solo shot in the third to help Ryan Dempster win his fifth straight start.
Dempster (11-6) improved to 6-1 since he was acquired by the Rangers on July 31. The right-hander allowed two runs and struck out eight in seven innings.
"I just try to do my job the same way, try to execute and make as many pitches as possible," Dempster said.
Cleveland starter Jeanmar Gomez (5-8) allowed five runs and six hits in four innings. Gomez, who won his prior two starts against Texas this season, has not pitched more than six innings in his last nine starts.
"(Gomez) didn't have good stuff and couldn't locate his pitches," Cleveland manager Manny Acta said. "They took advantage of it."
Joe Nathan, who has converted his last 31 save opportunities, pitched the ninth for his 33rd save of the season.
First-place Texas maintained a three-game lead in the AL West over Oakland, which beat the Los Angeles Angels 4-1.
Kinsler led off the bottom of the first with a double and scored on Hamilton's groundout to set the stage for a surging Beltre. Beltre hit a 1-0 pitch from Gomez over the fence in left to give the Rangers a 3-0 lead. It was his seventh home run in September.
Hamilton's 434-foot blast landed several rows deep in the upper deck in right field. He leads the majors with 41 home runs and 121 RBIs.
That was plenty of support for Dempster, who retired the last nine batters he faced. Dempster has a 1.91 ERA over his last five starts. His eight strikeouts were his most since joining the Rangers.
Notes: Texas RHP Roy Oswalt (right forearm strain) said he plans to throw on Thursday. He left his start early Sunday against Tampa Bay. . Indians SS Asdrubal Cabrera (sore right wrist) took batting practice Wednesday, but missed his third straight game. . Cleveland RHP Roberto Hernandez (right ankle) is out of his walking boot and is expected to throw a bullpen session early next week. . Texas' Mike Adams said he felt tightness in a muscle near his right shoulder Tuesday night and the reliever likely won't pitch the next two to three days. . Cleveland's Travis Hafner (back) is expected to take batting practice on Friday. . Texas opens the 2013 season at Houston, who will be playing their first season in the AL West. . Texas C Mike Napoli (strained left quad) hit a two-run homer and caught the entire game in a rehab assignment for Double-A Frisco.