Maybe a day off wasn’t such a bad thing for Conor Gillaspie. Both the third baseman and his manager suggested 24 hours of rest could have given Gillaspie an extra boost in Tuesday night’s 8-3 White Sox victory over the Boston Red Sox in front of 35,345 at Fenway Park. Gillaspie, who missed Monday’s game with a bruised right knee, had three hits, including a go-ahead, two-run home run, as the White Sox won their third straight and for the eighth time in 11 games. John Danks got through 5 2/3 innings to earn his fifth victory in seven starts and Ronald Belisario spearheaded a stout effort by the bullpen with 2 1/3 scoreless frames. “Sometimes you can benefit by getting hurt, getting a day off and recharging,” White Sox manager Robin Ventura said. “(Gillaspie) was fine. He came out today and hit early and he was fine. You can see he was swinging the bat fine.” Gillaspie, who carried a .788 OPS into Tuesday’s game, hadn’t been as good at the plate recently as he was earlier this season. In his past 10 games, Gillaspie was 5-for-35 with a homer and three RBIs. But he was forced out of the lineup for part of Sunday and missed all of Monday’s game with a bruised right knee after a pitch struck him. Even though he was still in some pain on Tuesday, Gillaspie told Ventura he was ready to play. He didn’t take long to show him he felt good. Gillaspie blooped a single to load the bases in a second-inning rally in which the White Sox scored twice without an RBI. Two innings later, Gillaspie doubled off the Green Monster and scored on Alejandro De Aza’s two-out RBI single to give the White Sox a 3-0 lead. That lead vanished when Boston scored three runs off Danks in the fifth inning. But Gillaspie got it right back in the sixth inning when he launched a two-run drive past Pesky’s Pole against Red Sox starter Brandon Workman (1-3), who allowed five runs (three earned) over seven innings.