After Jacoby Ellsbury opened the scoring with a two-run single in the second inning, Ortiz followed with a two-run double for a quick 4-0 Boston lead.
The Red Sox designated hitter also supplied what turned out to be the decisive run with a fourth-inning RBI single for a 7-4 Red Sox advantage.
Stephen Drew socked a solo homer for American League East-leading Boston, which won for the seventh time in eight games overall.
Brandon Workman (4-2) earned the decision and Koji Uehara secured the win with his 16th save.
Chisox starter Andre Rienzo (1-1) was roughed up for five runs over three full innings.
Conor Gillaspie knocked in a pair of runs and Tyler Flowers homered for Chicago.