Beltre, who was not in manager Ron Washington's initial lineup after missing a game with a gastrointestinal ailment, unloaded a two-run homer against Frieri in the top of the ninth inning to hand Darvish and the Rangers a 3-1 decision in front of 38,205 at Angel Stadium.
"Hitting that go-ahead two-run homer against their closer is something an outstanding player does -- and he did," Darvish said through an interpreter of Beltre, the Gold Glove third baseman who was serving as designated hitter.
"A couple of days ago, he was feeling very ill. We all saw that pain as teammates. To see him in the lineup gives the rest of us a lot of strength and courage to fight through these times."
It was the ninth series win in the past 10 for Texas, which maintained its four-game lead over the Athletics in the American League West.
Joe Nathan registered the save for Darvish, who climbed to 16-9 with his fourth consecutive win. The save was No. 34 for Nathan.
The Rangers maintained their four-game lead over the A's with 13 remaining, as their magic number for a third straight AL West title fell to 10.
The Angels fell 8 1/2 games behind the Rangers and 4 1/2 games out of the second Wild Card spot with a crushing loss. Frieri, who let a ninth-inning lead get away for Greinke in his previous start in Kansas City with a pair of homers, fell to 4-2.
Michael Young's leadoff single preceded Beltre's 34th home run, a drive into the left-field seats on a Frieri slider. The AL MVP candidate has 95 runs batted in.
"I'm supposed to help my team," Beltre said, having gone hitless against Greinke. "I didn't do anything my first three at-bats, so that was a chance to redeem myself.
"Most of the time I look for the fastball, and his is sneaky. He threw me a breaking ball and I hit it good. Yu pitched a tremendous game tonight. It's nice to get him a win."
Beltre talked his way into the lineup, pleading his case before the game.
"You can't keep him out of the lineup," Washington said. "He was just saying thanks for putting him in the lineup. I said there wasn't any doubt about putting him in the lineup. I didn't want to fight him.
"He's a special player, special person, special teammate. He's a gritty player. He has a passion for the game. He won't let his teammates down. His teammates feed off of that. He's a pro's pro."
Beltre looks for the fastball and reacts to the breaking stuff. Frieri didn't second-guess himself for the pitch selection, only the location.
"I just pitch," Frieri said. "That was the pitch that I wanted to throw. He hit it. Every pitch that I make is because I wanted to throw it. He hit a pitch, he's a good hitter, and that happens. Maybe I didn't execute the pitch where I wanted, but I wanted to throw that pitch.
"It was a slider. I was trying to go down and away. I left it a little bit up in the middle, and he put a good swing on it, and it went out of the park."
Darvish struck out nine in eight innings, allowing one run on four hits and a walk.
Greinke, the 2009 AL Cy Young Award winner with the Royals, was equal to the challenge. He held the Rangers to a run on five hits in eight innings, striking out eight with no walks.
Nelson Cruz singled leading off the fifth inning, taking third on David Murphy's hit-and-run single. Geovany Soto's fly ball to right was just deep enough, Cruz sliding home to beat Torii Hunter's strong, accurate throw.
Darvish took a one-hitter into the sixth when Mark Trumbo, after trying in vain to bunt for a hit, slammed a single through the middle. Pinch-runner Peter Bourjos moved to third on Chris Iannetta's single to right.
After rookie sensation Mike Trout struck out on a high, inside fastball, Hunter's slow roller to shortstop Elvis Andrus for a force at second cashed in Bourjos. Darvish retired Albert Pujols on a popup to quell the disturbance.
"He was actually the best I've seen him today," Hunter said of Darvish, who is 3-1 with a 4.33 ERA in five starts against the Angels. "Greinke had a tremendous game, too. Darvish was really good. Man, he threw the curveball, he threw the cutters hard, soft. He had the slider working. And he threw strikes. I'm not used to him throwing strikes."
Since getting knocked around in Boston on Aug. 6, Darvish has gone at least 6 2/3 innings in seven consecutive outings, his ERA plunging from 4.57 to 3.90.
Erick Aybar's walk leading off the third inning and Iannetta's single had runners at the corners with one out. But Trout struck out, and it became a double play when Soto nailed Iannetta at second.
"On the first one," Darvish said, reconstructing the two big strikeouts of Trout, "I was using a lot of different pitches, and he was kind of off. On the second strikeout, I had the intent of going up and in with a four-seam fastball. I don't think I've thrown that pitch at all to right-handed hitters with two strikes. If I miss in, I might hit him.
"Soto [came to the mound] and said, `Let's go with the four-seam fastball, in.' I said, 'OK, but up.' The four-seam was his call but throwing it up was mine."
Darvish finished with a flourish, striking out the side in the eighth.
"The line was very good," Darvish said, "but the detail -- command -- wasn't all that great."
The man from Japan must be a perfectionist.