That allowed the Rangers to snap a two-game losing streak after a 9-2 loss to the Red Sox in the three-game series opener on Monday night and they have now won five of their last seven.
"It was a good bounce-back win after last night," manager Ron Washington said. "It was certainly a big game. We didn't want to go down 0-2. Now we tied the series and have a chance to win it."
Dempster put them in that position with his first victory for a team that drafted him 17 years ago.
"It's awesome," Dempster said. "Drafted by the Rangers on June 1, 1995, I didn't think it would take this long, but it's a nice feeling."
Especially considering what happened on Thursday against the Angels.
"There was a lot of emotion in that first start," Dempster said. "I didn't do a good job of executing, but tonight I did much better. It comes down to executing pitches and I did a better job of it."
Catcher Geovany Soto, who was also acquired from the Cubs last week and has been behind the plate for both of Dempster's starts, said the difference on Tuesday night was being able to keep the ball down.
"He left a couple of pitches up early in the game, but after the second or third inning, he was really keeping the ball down and executing," Soto said. "In Chicago, that's what he was doing most of the time and he showed that tonight."
Dempster hooked up against Red Sox left-hander Jon Lester in a pretty good pitching duel. The Rangers were held scoreless on two hits through five innings before scoring two in the sixth and two in the seventh. They also added single runs in the eighth and ninth.
The Rangers had 10 hits, although just one for extra bases. That was a double by David Murphy to open the sixth. But in the final four innings, the Rangers worked three walks plus a hit batter, stole a base, got a run on a sacrifice fly and twice moved runners into scoring position with the hit-and-run. They were also 5-for-11 with runners in scoring position.
"We just worked some counts when we could," Murphy said. "Lester had great stuff. He has good stuff period and he was locating well. The umpire had a small strike zone tonight and that helped. We just tried to do whatever we could to put runs across. We just had a solid offensive game against a pitcher who has good stuff."
Dempster took a four-hit shutout into the seventh. With one out, Jarrod Saltalamacchia grounded a single through the right side just off first baseman Mitch Moreland's glove. After Mike Aviles flied out, Ryan Kalish hit a grounder that Ian Kinsler fumbled with a backhanded attempt for an error.
That brought up Middlebrooks, who was pinch-hitting for Nick Punto at the bottom of the order, and he crushed one just over the left-field wall for a three-run home run. The Rangers asked and got a review, believing a fan in the Green Monster seats leaned out and caught a ball that might have hit the top of the wall instead of clearing it. After the review, the original call stood.
Robbie Ross took over for Dempster and finished the inning with one pitch, getting Jacoby Ellsbury on a grounder to short. Mike Adams pitched a scoreless eighth and that left the ninth for Nathan.
Nathan, after getting four days off, was pitching for the first time since his back-to-back outings against the Angels on Wednesday and Thursday. He allowed a combined four runs and threw 62 pitches in those games, prompting the Rangers to give him a couple days off. He also wasn't needed Sunday or Monday so he was well-rested on Tuesday night.
Nathan gave up a leadoff single to Saltalamacchia but got Aviles to ground into a double play before striking out Kalish to end the game.
"It was just a matter of getting a little bit of time to allow my arm to get some life back into it," Nathan said. "After those last couple of outings, I knew I was achy and stiff and forcing the ball. Four days off all together, that definitely helps out. I felt a lot better, a lot sharper and a lot crisper."