"My first game ... it was great, but we didn't win," said Mazara, who finished 3-for-4. "It would have been better if we had won."
Mazara, called up to play right field while Shin-Soo Choo is on the disabled list, had a single in his first two at-bats, and then crushed a home run off Weaver to center in the fifth.
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"A memorable debut for the young man," Rangers manager Jeff Banister said. "Three hits and a home run ... that's a special day. Great poise, he walked up there in the first inning and didn't get caught up. He stayed with his approach."
Mazara is the fifth Rangers player to have three hits in his Major League debut, and the eighth to hit a home run on his first day in the big leagues.
"I knew nothing, really," Weaver said. "Not much about him. He kind of had a long swing, and he had a good approach. It took me more than three at-bats to figure him out. He dumped a couple in, did a good job of keeping his hands back, and the heater in -- if we're still calling it fastballs -- the pitch in to him was not a bad pitch."
Fastball would be a generous term for what Weaver was throwing on Sunday. His hardest pitch was 84 mph. But the Rangers managed just six hits and one walk, and Weaver was able to strike out four. He threw 84 pitches before leaving after six innings.
"It's kind of tough facing Jered," Banister said. "He is not what you see every day from our hitters. He has been a challenge. We had very limited opportunities. It's almost like facing a knuckleballer. The velocity is not there, but he makes pitches."
The Rangers were 0-for-7 with runners in scoring position. Weaver is now 11-0 with a 2.23 ERA in 18 career starts against the Rangers in Anaheim.
"He knows how to pitch," Adrian Beltre said. "Sometimes you would rather face a guy throwing 94 in the middle of the plate than guys who throw 80 on the corners. He knows how to paint. He is tough, especially in this ballpark. We couldn't find a way to put anything together."
The Rangers did have Mazara, but a rookie making a remarkable Major League debut was not enough for a win.