Beltre also scored twice as the Rangers rolled to their 10th win in 13 games and handed the reeling Indians their sixth straight loss.
Ryan Dempster (4-1) pitched two-hit ball over six innings, Michael Young had two of Texas' four RBI hits with two outs, and Joe Nathan got the final two outs for his 26th consecutive save and 28th overall.
"The guys executed in the clutch," Texas manager Ron Washington said. "Beltre was very good, and Dempster had a good changeup and slider, enabling him to move his fastball around."
Not everything went the Rangers' way. Right fielder Nelson Cruz was ejected for slamming his bat on the plate in the seventh after his third strikeout. After the game, lefty Robbie Ross, who is 6-0 with a 1.78 ERA in 52 relief appearances, was put on the disabled list with a strained forearm.
Beltre had three of his hits off Ubaldo Jimenez (9-14) as Cleveland's right-hander couldn't keep the Indians from losing for the 15th time in 16 games. Cleveland went 5-24 in August, tying the team record for losses in one month, set in July 1914. The Indians are 5-28 since July 27.
Beltre had two doubles and two singles. His only out came on a diving catch by left fielder Jason Donald in the ninth. The third baseman has hit .472 (17 for 36) with 14 RBIs in his last nine games. In his last 68 games, Beltre has batted .334 with 15 homers and 45 RBIs.
The Indians are as frigid as Beltre has been torrid, dropping to 11-36 in the second half. Cleveland has hit just .194 with runners in scoring position over that time and their starting rotation's 6.47 ERA during that span is the worst in the majors.
"For the most part, pitching sets the tone," manager Manny Acta said before the game. `You can scratch out runs here and there, but it is all about pitching."
As Acta's job falls further into jeopardy with each loss, he shook up the lineup to try and manufacture some offense. He reinstated Shin-Soo Choo into the leadoff spot, dropping Jason Kipnis and Asdrubal Cabrera one spot each to second and third.
"You've got to die trying, man," Acta said.
The Indians did just that against Dempster, who was perfect before issuing a one-out walk to Jack Hannahan in the third. Santana broke up the no-hitter with an RBI single in the fourth, when shortstop Elvis Andrus made two errors.
"He's been around," Acta said of Dempster. "He knows how to pitch. He uses both side of the plate. He's a veteran guy. He did a good job."
Dempster wasn't worried about facing Cleveland's left-laden lineup. Donald, at No. 9, was the only right-hander.
"Going left, right, left, right can be tougher," Dempster said. "When you have a lot of lefties, you can get into a groove with location. I can get more comfortable with my split."
Jimenez made 31 pitches in the first, but allowed only one run, on Beltre's RBI single.
Two innings later, his pitch count at 78, Jimenez trailed 3-0 after Young and David Murphy had consecutive RBI singles in the third.
Ian Kinsler's two-out RBI single on Jimenez's season-high 117th pitch made it 4-1 in the sixth.
The right-hander gave up eight hits, four runs and three walks. Though he struck out seven, he also dropped to 1-7 with 7.79 ERA in 10 starts since the All-Star break.
Young singled home Beltre in the seventh against reliever Esmil Rogers.
Dempster, who was only 5-5 despite a sparkling 2.25 ERA in 16 starts for the Cubs, is enjoying great run support in Texas. The Rangers lead the majors with 675 runs, and have scored 31 in Dempster's 37 1/3 innings since he was acquired on July 31 from the Chicago Cubs. He had not faced Cleveland since 2006, when he worked in relief for the Cubs.
Cleveland's 5-24 August ties the 1982 New York Mets and 1961 Washington Senators for the worst record in the month since 1944. ... Texas went 19-10 in August and is 23-6 against the Indians since the start of 2009. ... Andrus went 1 for 5. He has hit safely in all 27 of his career games against Cleveland. ... Texas C Mike Napoli, out since Aug. 11 with a strained left quad, has begun running, but it's unclear when he will return. ... OF Shelley Duncan was sent outright to Triple-A Columbus. The Indians had designated him for assignment on Wednesday. ... Cruz went 0 for 4 with runners in scoring position overall before his first career ejection, by plate umpire Bill Welke. ... Texas will call up six players when the rosters expand Saturday, including 19-year-old SS Jurickson Profar. He will be the first player born in 1993 to play in the majors when he debuts. ... Cleveland RHP Jeanmar Gomez will start Saturday in place of RHP Roberto Hernandez, who has a tender right ankle.