Actually, you can win without offense. You can also win without pitching. You generally lose when you don't have either. The Sox lost today because Peavy didn't pitch very well, and the offense couldn't overcome that. The Sox needed more from Peavy today because he obviously wasn't going to come out early to put more strain on the bullpen. Starters who walk in two runs with their team already losing by two generally don't stay in for two more innings. I am guessing that Ventura wanted a well-rested bullpen for Axelrod's start against the Red Sox
If Peavy was on, two runs would have been enough to win, even with a run in the ninth. The Sox beat the Angels scoring only two runs through eight and another in the ninth in Sale's start and scored nine runs in losing Santiago's start.