Ryan Dempster realizes his days with the Chicago Cubs could be winding down, particularly if he keeps this up. He’s dominating, and a contender just might want him.

Dempster pitched four-hit ball over seven innings, and the Cubs hung on to beat team president Theo Epstein’s former club, topping the struggling Boston Red Sox 3-0 on Friday.

“I’m not naive,’’ Dempster said. “I’m not oblivious to what’s going on.’’

The Cubs are in the early stages of their rebuilding process, and he could help a team eyeing the playoffs.

In his 15th season in the majors and ninth with the Cubs, Dempster has the right to veto any trade. He also has an expiring contract, and he’s pitching as well as ever.

“If I focus on that, I wouldn’t be doing a very good job as a teammate, and I wouldn’t be doing a very good job for myself if I wasn’t focusing on what I need to do,’’ Dempster said.

He sure was locked in on Friday, yet the Cubs had to hang on in the ninth.

The Red Sox loaded the bases against Carlos Marmol, but he got out of it when Dustin Pedroia forced the runner at third to end the game. That gave Marmol three saves in five chances and the Cubs a dramatic win after they cruised through the first eight innings.

Dempster (3-3) stretched his scoreless innings streak to 22 and lowered his ERA to 2.11 with another dominant performance.

He was at it again after shutting down Milwaukee and Minnesota. This time, the right-hander struck out three and walked two while winning his third straight start after going 18 in a row without a victory.

Dempster also helped himself at the plate with two hits. He won a $500 bet with Tony Campana when he came through with his second career triple past a diving right fielder Adrian Gonzalez and scored in the second to make it 3-0 after Steve Clevenger hit a two-run, bases-loaded double off Daisuke Matsuzaka (0-2) in the first.