The home run was the 603rd of his career but only his first since June 30 and just his second since June 22.
"It's been tough for me; I'm not going to lie to you," Sosa said. "But the thing I like is my teammates have been picking me up. I just have to keep working, and I know I'm going to get out of it. Today was a great day for me, and hopefully I can finish up strong."
Despite his struggles, manager Ron Washington has stayed with Sosa as much as possible as his cleanup hitter while giving him his usual days off.
"I was a baseball player," Washington said. "I know what it feels like to struggle. But Sammy still has the ability to drive in runs, and I'm not about to quit on that. He still leads our team in RBIs. I know what he's going through and I'm going to stick with him."
The double and the home run both came off Mariners left-hander Horacio Ramirez, and Sosa is now hitting .338 with four home runs and 25 RBIs in 74 at-bats against lefties this year.
That's significant from the Rangers standpoint. Most American League contenders are set at designated hitter, limiting the Rangers' options on who might be interested in Sosa. But if he continues to show he can still pummel left-handed pitching, then he might prove valuable to a team looking for a right-handed platoon outfielder or pinch-hitter.
"A lot of people talk about left-handers, but I think I'm able to hit against anybody," Sosa said. "I'm not afraid of anybody, lefty or righty."
The Rangers face two more left-handers in a doubleheader against the Mariners on Tuesday and another on Saturday when Odalis Perez pitches for the Kansas City Royals.
Sosa has talked about the desire of staying with the Rangers and beyond, and he has done everything they have asked of him. The Rangers have no desire to simply let Sosa go, but they wouldn't mind finding him the right home for the stretch run so they can call up Jason Botts from Triple-A Oklahoma.
The Rangers have made it clear they are not going to bring up Botts until they can get him consistent at-bats, and that's not likely to happen while Sosa is here.
"I've always said I'd like to finish my career here," Sosa said. "I've said that from the beginning. This is the team that gave me the opportunity. I feel good, but this is a business. I don't want to be traded, but if that happens I have no choice but to pack up my stuff and go."
Sosa made a winner out of Kevin Millwood, who almost suffered a first-inning knockout. But he survived that and managed to hang around for 5 2/3 innings to earn his fifth victory in his last eight starts.
Millwood started the night by giving up a single to Ichiro Suzuki, and then he walked Jose Vidro and Raul Ibanez to load the bases. Jose Guillen's single drove home two runs, and Adrian Beltre singled to reload the bases with still nobody out.
But Millwood struck out Richie Sexson and then got Kenji Johjima to hit a grounder right at third baseman Travis Metcalf for an inning-ending double play.
That kept it a quite manageable 2-0 game, and the Rangers were able to take the lead in the third. Metcalf doubled to left to start the inning and scored on a one-out single by Michael Young. After Mark Teixeira walked, Sosa put the Rangers ahead with a two-run double against the left-field wall.
The Mariners tied it in the fourth when Ichiro singled, stole second and scored on Vidro's single. But Sosa put the Rangers ahead for good with a three-run home run off Ramirez in the fifth.
The Rangers needed that and more because the Mariners almost pulled this one out against Eric Gagne in the ninth. Seattle trailed 8-4 going into the inning but scored three on Richie Sexson's homer and had the winning run on first base before Gagne finally put the game away.
"That was ugly," Gagne said. "I just couldn't make my pitches. I got the ball up and wasn't able to focus enough."
But as Washington said, "They got some runs off him, but he got three outs and that's all that matters."