Ramirez then told fans listening on the Red Sox Radio Network afterward that there's no doubt where he wants to keep playing for the foreseeable future.
"I feel good," said Ramirez, who added that he wants to stay in Boston for another four years.
Ramirez now has a Major League-leading nine go-ahead RBIs and an MLB-best six game-winning RBIs. He is now 14-for-30 in his last eight games with multiple hits in five of those games.
His confidence is building with every machine-like swing.
"Why not?" Ramirez said when asked if he feels he can keep it up. "I feel like a kid."
Early on, however, it was Texas starter Jason Jennings and slugging outfielder Josh Hamilton who were stealing the headlines.
Hamilton began his big night with a solo homer on a 1-1 pitch from Jon Lester with one out in the second, a line drive to the first row of Green Monster seats in left.
The Red Sox responded in the bottom of the inning when Jacoby Ellsbury led off with a double. After Jennings mishandled Dustin Pedroia's sacrifice bunt, Boston had runners at first and third and none out. Ellsbury scored on Ortiz's 4-6-3 double play.
Ramirez then walked, and Kevin Youkilis followed with an RBI double to right-center to give the Red Sox the lead, 2-1.
But Lester, who matched a career high by allowing 10 hits over 6 1/3 innings, surrendered the lead in the next inning when Adam Melhuse singled home David Murphy. Jason Botts doubled home Hamilton to give the Rangers a 3-2 lead.
Jennings then settled down, retiring 10 straight after walking Ramirez in the third and 13 of the final 14 batters he faced.
Joaquin Benoit (1-1) could not hold the lead for Jennings, allowing Ortiz and Ramirez to do their damage in the eighth.
Pedroia started it with a one-out, towering double off the wall in left. Ortiz followed with a line drive through the shift that Ian Kinsler knocked down but couldn't control, allowing Pedroia to score the tying run.
"[Ortiz is] going to come through," said Ramirez. "If he doesn't hit, I'm going to come through for him."
Ortiz's single brought Ramirez to the plate.
"In that situation, I'm not trying to do much," Ramirez said. "I'm just trying to get a good pitch to drive, and he gave it to me, and I did."
Ramirez wanted to see what kind of stuff the hard-throwing Benoit had on this night. He took the first pitch. He didn't need to watch another go by.
Benoit threw a changeup at the knees on the second pitch.
"I thought it was down," Texas manager Ron Washington said of the pitch. "He doesn't give a darn where it's at. And it wasn't just Boston's Fenway wall that it went over, because if it was any other ball park, I think it was gone, too."
"Especially when you have to pitch to David and you know Manny's coming up next, that's what keeps us in the ballgame at all times," Red Sox closer Jonathan Papelbon said. "If those guys are coming up late in the ballgame, those games are never over."
Papelbon gave up a leadoff single in the ninth, but earned his sixth save while Javier Lopez (1-0) notched his first win of the season.
"It's pretty impressive what he's doing right now," Papelbon said of Ramirez. "Regardless of what you say about that guy, he prepares better than anybody and is more focused than anybody as a hitter I've ever seen. That's incredible what he's doing right now."
Added Red Sox manager Terry Francona, "It's a pretty swing, isn't it? It's just nice to get the game tied. We have [Hideki Okajima] and Pap; we're at home. We didn't have the lead for very long, but it was long enough and it was at the right time."