Lackey (3-1) also walked a batter and hit another in the second to load the bases, but got Wood on a swinging strikeout to end the threat.
Daniel Bard worked the eighth and Jonathan Papelbon produced a perfect ninth for his eighth save.
Ortiz came into the contest with a .149 batting average, but had two hits and a walk. His solo homer came in the fourth and gave the Red Sox a 2-0 lead. Boston has won the first three of the four-game series.
Adrian Beltre also had a solo shot for the Red Sox in the eighth.
Los Angeles lost its sixth straight -- all on the road. Joel Pineiro (2-4) was charged with the setback, surrendering two runs on eight hits over six innings. He had given up 10 runs to Detroit in his previous outing.