Morales was acquired by the Mariners this year after spending his first eight years in the Angels organization.
"I have a lot of friends over there, but once I cross the lines, it's the game and it's business and we have to go out there and beat them," Morales said through interpreter Jaime Navarro.
Rookie right-hander Yoervis Medina picked up the first save of his career by shutting down the heart of the Angels lineup in order.
Bonderman allowed just one run and six hits in six innings against a team that had outscored Seattle 30-4 in its three previous games at Angel Stadium this season.
The former Tigers starter had a rough first Major League game since 2010 two weeks ago in Minnesota, but has since allowed just two runs over 20 innings against the Yankees, Astros and Angels. With the no-decision, Bonderman remains 1-1, with a 3.28 ERA.
Bonderman threw eight scoreless innings in his previous start against the Astros, but saw a 1-0 lead disappear when closer Tom Wilhelmsen gave up five runs in the ninth.
This time, Oliver Perez replaced Bonderman and threw a scoreless seventh, but Albert Pujols greeted Wilhelmsen with a leadoff homer in the eighth to tie the game at 2. Wilhelmsen wound up pitching 1 2/3 innings, putting the first two runners on in the ninth before striking out Peter Bourjos and getting Mike Trout to fly out to center.
Manager Eric Wedge then brought in left-hander Charlie Furbush, who struck out Josh Hamilton on five straight breaking balls to send the game into extra innings.
"I've faced him a couple times," Furbush said of his offspeed selection. "That's just something that has worked for me in the past against him, so I figured I'd go with my best pitch there and see how it turned out. Luckily we got the strikeout."
Bonderman didn't strike out any batters, but he induced three double plays from Hamilton, all three times eliminating leadoff hitter Trout.
"It was a tough outing. I really had to work," Bonderman said. "I wasn't hitting my spots the way I wanted to, but I made the pitches when I had to and was able to keep the team in the game and give us a chance to win."
And in the end, he enjoyed being a part of a victory that vaulted the Mariners a half-game ahead of the Angels into third in the American League West at 32-40.
"It's a team win," Bonderman said. "No matters what happens in this game, as a starter your job is to go out and give your team a chance to win. If I can do that, and guys can find to way to win, that's great. That's my job, that's what my role is. If I don't get the win, I don't care. I want to win as a team. I know what winning feels like it. It's fun. It's a great time. You enjoy being at the field. We're really close. We just have to put it all together and find a way to keep it going."
The Mariners hit back-to-back home runs off Joe Blanton in the second inning, with Raul Ibanez leading off with his 14th blast of the season and Justin Smoak following with his own shot just over the right-field fence.
Those were the only runs Seattle managed in 6 2/3 innings against Blanton, who allowed six hits and struck out a season-high 11 after coming into the game at 1-10 with a 5.87 ERA.
Smoak's blast came on the first pitch he saw following a 20-day stint on the disabled list due to a strained oblique muscle in his right side. It was Smoak's fourth homer of the year and first since May 20.
"It was good," Smoak said. "Raul going deep right there, then I was sitting dead red on the first pitch and I got a fastball and was able to put a good swing on it."
Smoak finished 1-for-4, with speedy center fielder Bourjos robbing him of a likely double on another well-hit drive in the left-center gap in the sixth inning.
Bonderman extended his scoreless-innings streak to a career-high-tying 14 before Mark Trumbo led off the second with a homer to left field. The Mariners then came back to win their first game in four tries at Angel Stadium this season.
"The guys did a great job of fighting," said Wedge. "Bonderman did a great job, then you work hard to keep the lead and they tie it back up. Especially when you're the visiting team, it can be tough. But our guys kept their cool, kept fighting through it. Morales had a tough night and then gets the huge hit. Seager with the big double there. Then you're using a guy that hasn't closed before. So it was a heckuva win for us."