Step by blazing step, it didn't take Amarista long to give Black and the rest of his team some much-needed hope.
''Then I saw Alexi's route, and you're sort of watching Alexi and watching the ball,'' Black said. ''And then in flight, you think maybe.''
Amarista ran backward on a dead sprint and laid out for a brilliant diving catch of the drive with two on and two outs to keep the game tied.
''When he hit it, I thought game over,'' Twins manager Ron Gardenhire said. ''We just watched their whole outfield move way in with two strikes, and he moved way in when that ball was hit, and Esco got a hold of it really nice, we thought he had no chance to catch that ball. But the young man ran it down, and it was a hell of a play.''
Smith had two hits and two RBIs. Joaquin Benoit picked up his fourth save in five tries and the Padres earned a split in the two-game series.
San Diego trailed 4-3 going into the ninth against Perkins, but Everth Cabrera tied the game with a sacrifice fly.
The Padres earlier in the day hired Texas Rangers assistant GM A.J. Preller as the team's new general manager, two people with knowledge of the situation told The Associated Press. The people spoke on condition of anonymity because an official announcement had not been made.
The speedy Amarista was a late-game defensive replacement, and what a move it was for Black. He raced a good 35 yards or more to track down Escobar's hit and the Padres bench erupted when he hauled it in.
Smith responded with a drive more than 400 feet off Anthony Swarzak (2-1) into the right-field stands for his 12th homer.
''It was nice to win a game like that,'' Smith said. ''Those are the games you need to win.''
Kevin Quackenbush (2-2) got the win.
Padres: Yangervis Solarte came up hobbling in the sixth inning after sliding home to tie the game at 3. Solarte appeared to actually roll over a bat laying in his way as he made the slide. But he was able to finish the game at third base.
Twins: Gardenhire said first baseman Joe Mauer and right-hander Ricky Nolasco both had successful debuts on their rehab stints with Class A Cedar Rapids on Tuesday night. Mauer (strained right oblique) was scheduled to play first base on Wednesday. If all goes well, Mauer will join the team in Houston next week.
Gardenhire said Nolasco (elbow) ''felt great'' after throwing 51 pitches. He will make at least one more start before being activated.
Padres right-hander Odrisamer Despaigne gave up four runs on eight hits with three walks and five strikeouts in 5 2-3 innings. It was his third straight outing allowing at least four runs and his third straight where he hasn't reached the seventh inning.
''He's been a little bit too up out over the plate for the most part,'' Black said.
YONDER HEATS UP
Alonso went 6 for 8 in the series to raise his average to .233. He was activated from the disabled list last week after dealing with right wrist tendinitis, and Black said he can see the difference.
''There's no soreness in his wrist,'' Black said. ''His forearms, his hands, everything having to do with gripping the bat feels good. His timing is there. He's one of the guys that we need to continue this hitting.''
Twins: Minnesota starts a four-game series in Oakland on Thursday night. RHP Yohan Pino (1-3, 4.57) pitches for the Twins against newly acquired A's LHP Jon Lester (11-7, 2.59).
AP Sports Writer Bernie Wilson in San Diego contributed to this story.