The Angels let a two-run lead get away in the ninth inning, depriving Weaver of what would have been his 14th win, and then prevailed on Rivera's second homer of the game and Kohn's superlative relief work in front of 43,149 on Friday night at Rangers Ballpark.
In the top of the 11th, Bobby Cassevah walked a batter and hit another. In came Kohn, who got a force at third from shortstop Romine with a sensational diving tag of the bag on Julio Borbon's hopper over third baseman Alberto Callaspo.
After Elvis Andrus struck out, Michael Young looked at a third strike, giving Kohn his first Major League save.
"It was awesome, getting the first save," Kohn said. "But the story tonight was Weav. It's unbelievable the way he pitches game after game. He's the definition of an ace."
Weaver's final strikeout victim was Young in the fourth. He finished with 233 strikeouts -- one more than Seattle's Felix Hernandez, who has been shut down by the Mariners. The Giants' Tim Lincecum has 231, but he's also not expected to throw another regular-season pitch.
Weaver would become the first Angels pitcher since Nolan Ryan in 1977 to win a Major League strikeout crown. The Express delivered 341 that season.
"That's almost two seasons of strikeouts," Weaver said, grinning.
His 224 1/3 innings are more meaningful than the 233 strikeouts, Weaver said, because it was his goal to reach 200 innings.
"It's cool," Weaver said of the strikeout title, "but it's nothing I really shot for. Coming down towards the end, knowing it could happen, that was exciting. It's something I'll be able to tell the grandchildren. The old man was pretty good back in the day."
Rich Thompson (2-0) claimed the win with Matt Harrison, victimized by Rivera's drive to left, moving to 3-2 with the loss. With wins in their final two games, the Angels can finish the season at .500.
Mitch Moreland, the Rangers' young first baseman, drilled a pair of solo shots against Weaver for a 2-1 Texas lead entering the eighth when the Angels stirred to life.
Facing reliever Michael Kirkman, Peter Bourjos' sacrifice fly scored Reggie Willits, who'd run for Mike Napoli after his walk and moved to third on Howard Kendrick's pinch single. Kendrick took second on the throw home and scored when Maicer Izturis punched an RBI single to right.
Rivera homered in the ninth for a two-run lead that got away under Fernando Rodney's watch.
The Angels' closer had Esteban German picked off for what would have been the final out in the ninth, but German got in a rundown and first baseman Rivera's throw sailed wide of catcher Jeff Mathis, allowing Moreland to score the tying run.
Bengie Molina's RBI single followed a hit batsman (Ian Kinsler) and walk (Moreland) by Rodney. After Borbon lined out softly for the second out, Andrus was at the plate when Rodney caught German moving -- and the Rangers escaped.
Moreland, who had tied it in the fifth with a blast to center, gave the Rangers the lead with a shot to right-center in the seventh, his ninth of the season.
Hunter unloaded an opposite-field homer in the fourth inning against Tommy Hunter to hand Weaver the lead. He had retired 14 in a row when Moreland launched his first missile to center with two away in the fifth.
Weaver had gone six starts and 48 1/3 innings between home runs.
"The last few times he faced us he has thrown the ball really well," Moreland said. "He mixes his pitches really well. I just wanted to get in a good hitting position, see the ball and hit it well."
Sidelined for 24 games with two fractured ribs, Josh Hamilton returned to the Rangers' lineup in center field and was 0-for-3.
With a diving stab in right center, Hunter robbed Nelson Cruz of extra bases with two on and two away in the sixth. But the play of the night belonged to the athletic Romine when he beat Moreland to the bag at third by an eyelash with a dive. Kohn thanked his buddy and struck out Andrus and Young to end it.
"Once he pulled back," Romine said, Borbon having bluffed a bunt, "I have to hold my ground in case he does swing. I needed everything I have to get there. I tried to stay on the outside and got the base. Sometimes they catch you by surprise and you have to react."