The San Diego Padres were last in the National League in average, runs, home runs and extra-base hits when they headed out for a 10-game road trip this past weekend.

They left Pittsburgh three days later with a sweep, their hitters having enjoyed a most productive stay at PNC Park.

Mat Latos allowed four hits in seven-plus innings and the Padres beat the Pirates 7-3 Sunday, capping a series in which they scored 35 runs — tying for the most in a single series in franchise history, the team said in citing the Elias Sports Bureau.

Just once in any three-game stretch in 42 years of major league baseball in San Diego had the Padres scored more than 35 runs.

"Offensively, the three games speak for themselves," Padres manager Bud Black said. "The collection of at bats from top to bottom were outstanding."

The Pirates, meanwhile, lost their 10th in a row. The loss completed an 0-7 homestand.

Will Venable had three hits and drove in two runs and Logan Forsythe had three RBIs as the Padres finished off their third sweep. San Diego has won four in a row.

Playing without top hitter Chase Headley, who sustained a broken left little finger on Saturday, the Padres continued their offensive renaissance at the hands of the beleaguered Pirates.

"We got off to a good start there, and some of their guys didn't have their best stuff," Venable said. "We consistently, throughout the lineup, put good swings on those mistakes and we were able to push some runs across."

Latos (6-11) allowed only two singles until Ryan Doumit and Pedro Alvarez singled to open the eighth. Brandon Wood followed with a home run off Chad Qualls.

Lack of run support been a familiar tale for Padres starters in recent seasons playing at spacious PETCO Park, and not many know that better than Latos, who had been given no run support in five of his first 21 starts.

The Padres had scored a total of 14 runs in his past six outings, leaving Latos without a win since June 27 despite a 3.26 ERA in that span. He had seven strikeouts and walked only one batter on Sunday.

"Everything was good," Latos said. "The fastball out of my hand was really good, the slider was really good, the curveball was good. I just got locked in and me and (catcher Luis Martinez) clicked and went after hitters."

Latos' mastery continued the misery for the Pirates, who completed a winless stay at PNC Park against the last-place Padres and Chicago Cubs, two teams that were a combined 39 games under .500 when the week began.

Pittsburgh was winless on a homestand of at least seven games for the first time in franchise history, STATS LLC said. No team in the majors has had a homestand that long without a win since Kansas City in May 2006.

"It's obviously not easy right now," second baseman Neil Walker said. "As baseball players, we've all gone through some sort of stretch like this, whether it was from a personal or a team standpoint. Nobody likes the feeling that we have right now.

"It's easy to let yourself go to a negative place when you're like this, but... we're still playing the same game we did when we were winning games. It's just been a little tougher for us."

Try a lot tougher. The Pirates, in first place in the NL Central on July 26, were outscored 59-25 by the Cubs and Padres. The bad week came after they got swept in Philadelphia.

A day after the Pirates held a players-only meeting following a 13-2 loss, they trailed 7-0 going into the bottom of the eighth.

The Padres got a run on a wild pitch by Daniel McCutchen and another that was set up by catcher Doumit's throwing error on a pitchout, two plays that exemplified Pittsburgh's recent futility.

This is the Pirates' longest losing streak since a 12-game slide June 6-18, 2010, a season in which they lost 105 games.

The crowd of 35,601 meant a total of 112,618 saw the series, the fourth-largest in PNC Park history. While fans on Friday and Saturday often resorting to booing, Sunday's scene never got ugly. Pirates fans were even given a reason to cheer when Wood's homer, his seventh, cut San Diego's lead to 7-3.

Pittsburgh's Xavier Paul then singled with one out, but Qualls got the Pirates' two best hitters, Andrew McCutchen and Neil Walker, to ground out harmlessly to end the inning.

Forsythe, in the lineup to replace Headley at third base, had an RBI groundout in the second against Kevin Correia (12-10) and a two-run single in the sixth. Venable added a two-run double in the eighth.

Signed in the offseason as a free agent from San Diego, Correia had allowed one run on three hits through 5 2-3 innings before running into two-out trouble in the sixth. He was charged with four runs on five hits and four walks, falling to 2-8 at home this season.

"I threw the ball pretty well up until there were two outs and nobody on in the sixth," Correia said. "It's just hard, in the situation we're in and the results of the games, to feel good about anything."

NOTES: Headley will travel back to San Diego to be examined by the Padres' team physician, along with hand specialist. ... The Padres improved to 25-17 in day games (they're 26-47 at night) and have won six consecutive series finale. ... Padres RHP Tim Stauffer is making his first career start in New York against the Mets on Monday.