Charlie Furbush (1-3) faced only one batter to get the victory, striking out Josh Hamilton with runners at first and second to end the ninth. Rookie Yoervis Medina got three outs for his first major league save.
Kyle Seager sparked the winning rally with a two-out double in the 10th against Garrett Richards (2-4). Morales, who struck out his previous three times up, then lined a 3-2 pitch off the glove of shortstop Erick Aybar to give Seattle the lead.
It was only the third RBI for Morales in 30 at-bats against the Angels since he was traded to the Mariners in December for pitcher Jason Vargas.
Seattle grabbed the lead on consecutive homers by Raul Ibanez and Justin Smoak in the second inning against Joe Blanton. But Mark Trumbo connected in the bottom half, and Albert Pujols tied it with a leadoff drive against Tom Wilhelmsen in the eighth.
Hamilton grounded into a double play his first three times up and struck out his next two at-bats. The 2010 AL MVP, who signed a five-year, $125 million contract in December, is batting .213 with 10 homers and 24 RBIs in 69 games.
Jeremy Bonderman pitched six innings of six-hit ball and Oliver Perez got three outs before Wilhelmsen yielded Pujols' 12th homer on an 0-1 pitch. Until then, right-handed batters were only 5 for 48 against Wilhelmsen, who had not allowed a home run this season in 29 1-3 innings.
The 30-year-old Bonderman, who missed the previous two seasons due to injuries, is 1-0 with a sparkling 0.90 ERA over 20 innings covering his last three starts. The Mariners signed him to a minor league contract in January.
The Angels, who outscored Seattle 30-4 in the previous three meetings, got their first run when Trumbo drove Bonderman's first pitch of the second into the rock pile in left-center for his team-high 16th homer and first since June 1. It ended Bonderman's streak of 14 consecutive scoreless innings, equaling his career best from 2007 with Detroit.
Blanton gave up six hits in 6 2-3 innings and tied a career high with 11 strikeouts, following an eight-day stretch between starts to work with pitching coach Mike Butcher on his fastball command.
Blanton, whose no-decision left him at 1-10, still shares the major league lead in losses with former Philadelphia Phillies teammate Cole Hamels. He has a 5.62 ERA in his first 14 starts with the Angels after signing a two-year, $15 million contract in December.
Ibanez led off the second with his 14th homer. Smoak, who came off the disabled list Tuesday after missing 18 games because of an oblique strain on his right side, then went deep for his fourth of the season.
Smoak's drive landed in the first row above the 18-foot right field wall. Angels manager Mike Scioscia came out to suggest fan interference to the umpires, but the ruling was upheld after a video replay.
NOTES: It was only the second time in 806 major league games that Hamilton grounded into more than one double play. He did it twice on June 18, 2010, with Texas at Boston. ... Ibanez has hit safely in his last 13 games at Angel Stadium one off his career best streak at this ballpark. His first career homer off Blanton came in his 50th at-bat against him. ... The Angels have scored no more than three runs in any of Blanton's last 10 starts while he was still in the game. ... The Angels have played in a major league-high 26 games that were decided by a one-run margin (10-16). ... The Mariners have hit 49 home runs on the road, compared to 29 at Safeco Field. ... Mariners reserve 1B Alex Liddi was optioned to Triple-A Tacoma to make room on the roster for Smoak.