Lance Berkman and David Murphy homered in the first off Weaver, putting the Rangers ahead to stay on the way to a 7-3 victory Sunday night after Darvish had allowed two quick runs only five nights after coming within one out of a perfect game.
"I didn't have everything today. It wasn't my 100 percent, but I had to grind it out," Darvish said through his translator. "The reason I was able to do that was because of all the support from my teammates."
While there were some social media reports that Hamilton made an obscene gesture to fans in right field, the five-time All-Star and 2010 AL MVP who played in the Rangers' only two World Series said that never happened.
"I never would do that. Ever. I never would flip anybody off," said Hamilton, expressing surprise about the constant booing every time he came to the plate. "A little more hectic than I expected. ... A little disappointing more than anything."
Hamilton, who signed a $125 million, five-year deal with the Angels last winter, finished 3 for 13 in the series, and is batting only .160 (4 for 25) on the season.
In an early-season matchup of aces, neither Darvish nor Weaver made it past five innings. But that wasn't because of the runs they allowed.
Darvish (2-0) threw 85 pitches over five innings, and was replaced starting the sixth because of a blister on his right ring finger that also had developed in the game against Houston when he retired 26 consecutive batters before giving up a single.
"As far as it developed, I don't really want to talk about it," said Darvish, describing it more like a piece of skin coming off than a blister. "We won the game, so I think everything went well."
Weaver (0-1) did throw to a batter in the sixth, but strained his left elbow when trying to dive out of the way of Mitch Moreland's liner to start the inning.
While Weaver avoided being hit by the ball, he landed awkwardly on his left arm. The pitcher immediately grabbed his arm near the elbow and manager Mike Scioscia and a trainer quickly were on the field. X-rays were negative.
"Pretty painful. It feels a little swollen in there," Weaver said after the game. "I can't move it around too good right now. It's strange. Kind of like jamming your thumb."
Weaver said he "didn't feel anything pop or crack," but said he wasn't sure if he'd make his next scheduled start.
Darvish had 14 strikeouts with no walks in his near perfect opener at Houston, but after a strike on the first pitch to leadoff hitter Mike Trout, he threw four straight balls. Darvish then hit Erick Aybar on the foot and walked Albert Pujols before a run scored on Hamilton's double-play grounder. Mark Trumbo's RBI single quickly made it 2-0.
Berkman' first homer with the Rangers was a two-run shot in the bottom of the first. Murphy added a solo shot two batters later to put Texas ahead to stay.
"I don't think you want to linger down to a team like that," said Berkman, who has hit in all six games and his batting .450.
Darvish retired only two of the first nine Angels he faced. The second time through the lineup, the ace from Japan had five strikeouts.
"Yu Darvish really did good damage control there," Texas manager Ron Washington said. "Yu settled down and kept us around until we were able to put some more runs on the board."
Darvish finished with six strikeouts, four walks and a hit batter. He gave up three runs and six hits over his five innings.
Mark Lowe, another former Ranger who heard boos, replaced Weaver on the mound. After a sacrifice bunt by Geovany Soto, Lowe walked No. 9 hitter Leonys Martin before Kinsler's third homer of the season, a three-run liner just over the right-field wall.
Weaver allowed five runs and seven hits in five innings. He struck out two and walked four.
Texas went up 4-2 in the fourth when Soto, the playing catcher for the first time this season, had a leadoff double. He scored on Kinsler's single.
The Angels got that run back in the fifth when Hamilton singled and scored on a double by Trumbo.
Robbie Ross, Tanner Scheppers and Joe Nathan combined for four scoreless innings in relief of Darvish. ... After opening the season with series at Cincinnati and Texas, both of Hamilton's former major league teams, the Angels play their home opener Tuesday against Oakland. Los Angeles is the first team since 2007 to open the season with three series in a row against playoff teams from the previous season. ... Soto was the last Rangers player on the opening-day roster to get in a game.