Hellickson (3-0), who held Los Angeles hitless in six at-bats with runners in scoring position through the second, allowed one run and five hits. Zobrist hit a solo shot off C.J. Wilson (2-2) during a two-run third.
"I definitely needed that one," Zobrist said. "It's the start of the season. April has not always been the greatest month for me. Hopefully I'll get it going a little bit. The good thing is we've been winning. When you're winning games, things are going well. You just keep working hard."
The Rays have won four in a row and six of seven.
Albert Pujols went 0 for 3, including two strikeouts, extending his hitless streak to 19 at-bats. The Angels slugger has not had a hit in five consecutive starts, which is the longest stretch in his big league career, but did walk in the eighth.
Pujols, with 445 homers, has not gone deep in 18 games this season, a span of 72 at-bats.
Los Angeles got a homer from Vernon Wells. Wilson gave up two runs, six hits, two walks and struck out 11 over seven innings.
"We have a lot of veteran hitters in this lineup that know what they need to do," Angels manager Mike Scioscia said. "It's just matter of executing."
Fernando Rodney, the third Rays reliever, pitched the ninth for his sixth save. The right-hander allowed an unearned run when Zobrist was charged with an error at second for misplaying Erick Aybar's grounder that allowed Torii Hunter to score with two outs.
"You never want to make an error in the ninth inning with the game on the line," Zobrist said. "It was a tough one. I haven't spent much time in the infield yet, and still I'm still getting comfortable."
Los Angeles, 6-12 this season, has lost six of eight.
"I really feel like we're close ... close to breaking through," Wilson said.
Jeff Keppinger added an RBI double in the third.
Wells cut the deficit to 2-1 on a fourth-inning homer. It ended a stretch of 55 1/3 innings that Tampa Bay had not allowed a home run.
Bobby Abreu had a leadoff double in the first, but was left stranded when Hellickson retired the next three batters, including Pujols, who hit a one-out grounder between short and third into a three-man infield defensive shift.
Hellickson also worked out of a bases-loaded, one-out jam during the second by striking out Chris Iannetta and getting Abreu's broken-bat grounder to third.
"I thought he looked more like himself," Rays manager Joe Maddon said.
After Iannetta walked to start the fifth, he was then thrown out trying to steal second after Abreu struck out swinging on a 3-2 pitch.
Los Angeles was 0 for 10 with runners in scoring position.
"You can't sugarcoat that part of it," Scioscia said. "It's critical to us. We need to bring that level up to support our pitching. There's a lot of situational hitting that has to be part of this club, and hopefully that's going to emerge."
Tampa Bay had four solo homers -- all off Ervin Santana -- in Tuesday night's 5-0 victory over Los Angeles. ... The Angels have been out-homered 23-12 this season. ... Wilson's career-high for strikeouts is 12. ... Los Angeles RHP Jerome Williams (1-1) and Rays' LHP Matt Moore (0-1) are the scheduled starters in Thursday's series finale.