''It always helps, obviously, when I can contribute to a team victory,'' said Alvarez, who's hitting .232 with 12 homers and 38 RBIs.
''I've always said sometimes results aren't indicative of how you may feel at the plate, and I feel like I'm a good place,'' the slugger added. ''I'm just going to continue to work.''
Andrew McCutchen went 3 for 5, drove in two runs and stole two bases for the Pirates in a homecoming of sorts for last year's NL MVP, who grew up in nearby Fort Meade and had never played before at Tropicana Field. He also scored twice in Pittsburgh's first appearance in St. Petersburg since 2003.
Alvarez, who hadn't homered since June 3, went deep off Alex Cobb (2-6) during a four-run fourth inning that also featured the first of McCutchen's two RBI singles. The first-pitch, 419-foot drive over the wall in center field snapped a season-high 16-game stretch without a homer - Alvarez's longest since a 22-game drought that began in September 2012 and extended into last season.
''A lot of times people have been taking their chances with Pedro, and he's an important part of our offense,'' Pirates manager Clint Hurdle said. ''We need him to fire, we need him to drive in runs and that was very good to see. Three-run homers always play well.''
Volquez (5-6) allowed five hits in a season-high eight innings.
James Loney drove in Tampa Bay's only run with a two-out, first-inning single, and the Pirates supported their starting pitcher by turning three double plays.
''I got a lot of help,'' Volquez said.
The Pirates climbed to .500 (38-38) for just the second time since April 17, when they were 8-8. They have won four of five following a three-game skid and are a NL-best 26-18 since May 6.
Tampa Bay has dropped 19 of its past 27 and is saddled with the worst record in the major leagues at 31-47.
''I feel like with every loss it's an opportunity missed,'' Cobb said, adding if the Rays are going to turn their season around they've got to get on a roll soon.
McCutchen, who is batting .366 in June, boosted his average in 11 interleague games to .425 with nine walks, four doubles and seven RBIs. His run-scoring single off Cobb moved him ahead of Brian Giles for the Pirates career record for RBIs in interleague action with 52. He added another in the ninth off Kirby Yates.
Alvarez, meanwhile, is hitting .317 with two home runs and eight RBIs against AL teams this season.
Cobb, making his seventh start since spending five weeks on the disabled list with a left oblique strain, allowed six runs and six hits in five innings.
Volquez won for the third time in his last five starts. The right-hander walked two, struck out one and didn't allow a hit after the fourth inning.
Three of Tampa Bay's six hits were infield singles, including Kevin Kiermaier's second-inning bunt. Jeanmar Gomez pitched the ninth for the Pirates, yielding a two-out single to Loney.
NOTES: Pirates OF Starling Marte was back in the lineup after missing two games tending to a personal matter at home in the Dominican Republic. ... Pittsburgh RHP Gerrit Cole (right shoulder fatigue) threw 83 pitches over six innings in a simulated game and could rejoin the rotation this weekend. ... Pirates 2B Neil Walker (appendectomy) is expected to be reinstated from the DL Tuesday. ... The Rays haven't announced if RHP Jeremy Hellickson (elbow) will need one more minor league start before returning. .. Tampa Bay 1B-OF Jerry Sands has a wrist injury, which Rays manager Joe Maddon said could require surgery.