His throwing error led to the run that put the Atlanta Braves ahead to stay, and they beat Miami 6-4 Tuesday night.
Alvarez (0-1) allowed five runs, four earned, in six innings. He missed the first three months of the season because of shoulder inflammation.
In the sixth inning, Alvarez fielded pitcher Julio Teheran's swinging bunt and threw wildly past first for an error, allowing B.J. Upton to score from second base. The unearned run put the Braves ahead 5-4.
"What we've seen is when we make a mistake, they've been able to make us pay for it," Marlins manager Mike Redmond said. "We gave them a run there on the error, and we don't have enough offense to give away runs."
The Marlins, who have the NL's worst record, lost their fifth game in a row.
Miami's Rob Brantly hit his first home run of the season, a three-run shot with two outs in the second. The runs were all unearned because they scored following a one-out error by third baseman Chris Johnson.
Atlanta bounced back and scored twice off Alvarez in the third to make it 3-all.
"Henderson had to really work out there," Redmond said. "Brantly came up big with the three-run home run, and we always talk about those shutdown innings and how important they are after you score to shut down the opposing team, and he just wasn't able to do that tonight.
Alvarez didn't talk to reporters after the game.
Justin Upton homered, doubled twice and scored three runs to help the Braves earn their 27th comeback victory, most in the NL. They overcame deficits of 3-1 and 4-3.
Pitchers for the two teams combined to retire 30 consecutive batters Monday, when Atlanta won 7-1 in 14 innings. The second game of the series was a slugfest by comparison, with Justin Upton leading the way.
He doubled home a run in the third, doubled and scored to make it 4-all in the fifth, then hit his 16th home run—but first since June 12—leading off the seventh against reliever Ryan Webb.
In Monday's marathon, Upton hit a two-run double to put Atlanta ahead in the final inning.
"He's starting to swing it like he did early in the season," Braves manager Fredi Gonzalez said. Upton had 12 homers after just 23 games.
Teheran (7-4) allowed one earned run in 7 1-3 innings. All-Star closer Craig Kimbrel pitched a perfect ninth for his 24th save in 27 chances, and Atlanta improved to 12-2 at Marlins Park since it opened in 2012.
Brian McCann had a sacrifice fly and an RBI single for the Braves. B.J. Upton raised his average to .178 with two hits and was robbed of an RBI single on a leaping grab by third baseman Ed Lucas.
"I'm starting to feel a lot better at the plate and hitting the ball hard," B.J. Upton said. "They're not always going to fall, but I'm starting to see my work pay off, and I definitely feel a lot better up there."
The Braves went ahead in the second when Freddie Freeman led off with a double, advanced on a groundout and scored on B.J. Upton's sacrifice fly. That was Upton's 20th RBI in 266 at-bats.
Brantly pulled a homer just inside the right-field foul pole in the second to put Miami ahead 3-1. Atlanta tied the score in the third on an RBI double by Justin Upton and a sacrifice fly by McCann.
"We started nitpicking the strike zone a little too much, and started getting in hitters' counts," Brantly said. "That hurt us."
Miami regained the lead in the third on an RBI single by Logan Morrison, who had been 2 for 17 with runners in scoring position. The Braves made it 4-all in the fifth when Justin Upton doubled and scored on McCann's single.
Marlins rookie center fielder Marcell Ozuna threw out Johnson trying to score on a flyout in the fourth inning. The assist was the eighth for Ozuna, one off the major league lead for outfielders.
NOTES: Braves RHP Brandon Beachy (elbow) allowed three hits and two runs in three innings during a rehab start for Triple-A Gwinnett against Norfolk. ... Before the game, the Marlins recalled LHP Duane Below from Triple-A New Orleans. ... The retractable roof was closed after being open at the start of Monday's game.