Dempster (3-3) allowed four hits and walked two while striking out three over seven innings in getting the win.
James Russell retired all three batters he faced in the eighth. But closer Carlos Marmol allowed the Red Sox to load the bases on a single, an error and a walk before he got a force out to end the game and pick up his third save.
Boston starter Daisuke Matsuzaka, making his second start as he comes back from so-called Tommy John surgery, allowed three runs and four hits in six innings. He also walked three and struck out three. All of the runs came in the first two innings.
Matsuzaka walked Cubs leadoff batter Tony Campana. He got two outs but walked Alfonso Soriano and Bryan LaHair. Steve Clevenger followed with a double down the left-field line that knocked in two runs.
Dempster tripled -- his second in his career but first since 2002 -- in the second and scored on a David DeJesus single.
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