The defending World Series champion Red Sox blew a 4-0 lead before Holt put them ahead again by hitting his third homer of the season. The ball sailed over right fielder Hunter Renfroe and bounced off the top of the wall and into the seats.
"Obviously you don't want to get too deep into the count against him and you don't have to deal with the splitter," Holt said. "Fortunately I was able to get a good pitch on that first one and put a good swing on it. I knew I hit it good but I kind of hit it high and I saw Renfroe drifting back kind of slow. It kind of scared me for a little while and then he jumped up and luckily it hit the top of the wall and had enough to get out."
Yates (0-4) leads the majors with 36 saves but has allowed a run in five of his 12 non-save situations. It was only the second homer he's allowed this season.
"Make a bad pitch, the guy hits it out of the park," Yates said. "It happens. I've got to make better pitches. I've given up some runs with a cushion. There's no margin for error when you got a tied ball game. Just the way it is.
"It's first pitch of the inning. I don't think that's ever happened for me, personally. I don't think I've ever come in a game and given up a home run first pitch of the inning in a tie game."
Manager Andy Green said Yates has been "sensational. Of course in the major league baseball season you have an outing or two that's not perfect. He's been able to battle through so many of them. ... We have obviously total confidence in him to keep giving him the baseball."
The Red Sox, who used six relievers, have beaten the Padres in seven of their last eight meetings and lead the overall series 14-6.
Boston has won seven of eight games and is six games out of the second AL wild card spot, with Oakland ahead of it.
"Obviously everybody knows where we're at," Holt said. "We've got to win as much as we've can. I feel like we've been playing good baseball, so we've got to keep going."
Luis Urias opened the seventh with a walk and advanced when pinch-hitter Francisco Mejia was hit by a pitch by Ryan Brasier, who was replaced by Josh Taylor. Rookie pinch-hitter Ty France singled to left to bring in Urias with the tying run. The Padres loaded the bases with two outs before Eric Hosmer struck out.
Mookie Betts started the scoring for the Red Sox in the third when he singled in Brock Holt, who was hit by a pitch.
The first four Boston batters reached in the fourth. J.D. Martinez singled, Andrew Benintendi walked and Christian Vazquez brought them both in with a double to center. Mitch Moreland singled in Vazquez.
The Padres closed within one run in the third, which was highlighted by Hosmer's two-run home run to right, his 19th, that chased Eovaldi. Manny Machado was aboard on a leadoff single. Marcus Walden came on and allowed a double by Renfroe, who advanced on Manuel Margot's fly ball to center and scored on Urias' groundout.
Eovaldi allowed two runs and four hits in three-plus innings, struck out three and walked one.
Lamet allowed four runs and six hits in five innings, struck out five and walked three.
The Padres had TV broadcasters Don Orsillo and Mark "Mud" Grant throw out the ceremonial first pitches. Orsillo spent 15 seasons calling Red Sox games before he was fired. He's in his fourth season calling Padres games.
Red Sox: LHP Brian Johnson (1-2) is scheduled to start the series finale Sunday.
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