ST. PETERSBURG, Fla. -- An outstanding pitching duel ended on one errant pitch.
Joyce opened the 10th with a double off Fernando Rodney (0-1). After Ben Zobrist lined out and Casey Kotchman moved Joyce to third with a grounder, Rodney threw a 1-2 pitch into the dirt well off the plate that eluded catcher Hank Conger.
"Hank did all he could," Angels manager Mike Scioscia said. "That would have been an incredible stop."
Rays manager Joe Maddon gave credit to Kotchman for advancing the runner and the lead Joyce got on third before the wild pitch.
"Especially with a guy like Rodney. He's going to throw some balls in the dirt," Maddon said.
The Rays, at 15-12, are the first team to finish April with a winning record after opening the season with a six-game losing streak.
Tampa Bay's James Shields took a shutout into the ninth before giving up a double to Torii Hunter to open the inning. Kyle Farnsworth came in and Hunter later scored to tie it at 1 on Howie Kendrick's grounder.
Farnsworth had converted all five of his previous save opportunities this season. The right-hander was OK after taking Vernon Wells' grounder in the ninth off his shin.
Joyce also homered for the Rays, who have won six of seven. Joel Peralta (1-0) struck out two during a perfect 10th.
Angels right-hander Joel Pineiro gave up one run and four hits over seven innings in his first start this year. He started the regular season on the 15-day disabled list due to right shoulder tightness.
Shields allowed one run, six hits, one walk and tied a career-high with 12 strikeouts in eight-plus innings. He had a stretch of 21 scoreless innings end.
"Outstanding, once again," Maddon said.
Shields was coming off consecutive four-hit victories over Toronto and the Chicago White Sox. The pair of wins, in which the right-hander allowed just one run, followed a stretch of nine straight winless starts, dating back to last year.
Joyce made it 1-0 on his homer leading off the fifth. He had a three-run shot, his first home run of the season, in Friday night's 8-5 loss to the Angels.
Shields was perfect through one out in the fifth when Kendrick singled to left. The Angels then loaded the bases on singles by Erick Aybar and Conger, but Shields recovered to strike out Peter Bourjos and Alexi Amarista.
"Both guys were matching each other pitch by pitch," Scioscia said. "We had some opportunties in the fifth. Just couldn't get a hit to change the course of that game."
Kendrick went 2-for-4 and has 49 hits in 108 at-bats overall against Tampa Bay.
Pineiro retired eight in a row to begin the game before Reid Brignac's third-inning single.
Angels RHP Jered Weaver (6-0), Sunday's scheduled starter, has a chance to become the majors first pitcher to go 7-0 through May 1st since Sadie McMahon was 9-0 in 1891 for Baltimore of the American Association. ... Maddon is hopeful that INF Sean Rodriguez (dislocated left pinky finger) will be able to avoid going on the disabled list. ... Los Angeles 3B Maicer Izturis, limited to one at-bat over the previous four games due to a sore left hamstring, was back in the starting lineup. ... Rays LF Sam Fuld went 0-for-4 and is hitless in his last 18 at-bats. He stayed in the game after fouling a bunt attempt off his forehead. Maddon said reports immediately after the game were that Fuld is fine.. ... Bourjos extended his hitting streak to 12 games with an eighth-inning single. ... The Rays recalled RHP Alex Cobb from Triple-A Durham to start Sunday's game. LHP Jake McGee was optioned to the International League club.