Howie Kendrick then hit a liner back to the mound that hit Cole on the upper left thigh, but he stayed in the game.
"It's pretty sore," Cole said. "Got me right on the thigh. Good thing I've got fat legs."
The Angels finally chased Cole on Alberto Callaspo's RBI single, and the Anaheim crowd cheered the local kid on the way to the dugout.
Weaver hasn't been his usual dominant self in five starts since returning from a 45-day stint on the disabled list. After he gave up Alvarez's 17th homer to lead off the second inning, Mercer followed with a two-run shot, his fourth of the season.
"The last three starts it just kind of seems like there's one inning that's a blow-up inning, and I've just got to learn to stay away from that," Weaver said. "It's frustrating. I'm not doing a whole lot to help the team right now. I just have to keep battling, and hopefully things will turn around."
The Pirates added another run in the fourth when Bourjos, normally a spectacular fielder, lost track of Starling Marte's two-out fly to center. The ball landed well behind him for an RBI triple.
Josh Hamilton sat out with a sore right wrist, and the $125 million slugger isn't likely to start a game this weekend while the Angels give him some rest. Hamilton, who was available off the bench, was in a 3-for-26 skid in the first seven games of the Angels' homestand.
NOTES: Pittsburgh improved to 2-5 at the Big A, getting its only previous win here on June 11, 2002. ... RHP Billy Buckner, selected from Triple-A Salt Lake before the game to take injured Jason Vargas' roster spot, pitched 2 2-3 sharp innings of relief for Weaver, giving up one hit and one walk. ... Mike Trout went 0 for 4, but made a full-stretch diving catch on Gaby Sanchez's drive into the left-field corner in the fifth.