The Red Sox loaded the bases against Carlos Marmol in the ninth, 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.
Dempster (3-3) stretched his scoreless innings streak to 22 and lowered his ERA to 2.11 with another dominant performance.
The Gibsons, B.C., native 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 drove his second career triple 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, sending Boston to its eighth loss in 11 games.