It was Boston's third straight win over the Angels, who have lost the first six games on a 10-game road trip. It's the first time the Angels have opened May at 0-5 in team history.
Adrian Beltre homered and drove in two runs for the Red Sox. Brandon Wood hit a solo homer off Lackey.
The Red Sox can complete the four-game sweep when Daisuke Matsuzaka faces Scott Kazmir on Thursday night.
Lackey (3-1) left the Angels in the offseason and signed an $82.5 million, five-year contract with Boston. He posted the Angels' highest winning percentage in team history at 102-71.
The right-hander played for the organization from 2002-2009 and was the first rookie to win Game 7 of a World Series since 1909, getting the victory when the Angels beat San Francisco in the 2002 decisive game.
Lackey 12 of 14 outs on grounders as he cruised through the middle innings. He walked two and struck out four overall, allowing Kendry Morales' single leading off the second as the only other hit.
Daniel Bard pitched a perfect eighth before Jonathan Papelbon worked the ninth for his eighth save.
Ortiz, back in the lineup as the DH despite an 0-for-4 game on Tuesday with two strikeouts and two double-play grounders, homered into the Green Monster seats against Joel Pineiro (2-4) seats to give Boston a 2-0 lead in the fourth. The struggling slugger entered hitting just .149.
Wood homered into the first row of the Monster seats in the fifth.
Beltre made it 3-1 against Brian Fuentes in the eighth.
The Red Sox had taken a 1-0 lead in the second when Beltre's bouncer down the third-base line hit the bag and rolled into short left for a single, scoring J.D. Drew from second.
Los Angeles left fielder Hideki Matsui threw out Marco Scutaro at the plate, trying to score on Kevin Youkilis' seventh-inning single.
The Angels came very close to turning a triple play in the second. With runners on first and second, Jeremy Hermida lined to Pineiro, who fired to second, doubling off Ortiz. Beltre barely slid into first safely ahead of shortstop Erick Aybar's throw and Angels manager Mike Scioscia came out to argue the play.
Notes
Terry Francona managed his 1,000th game with the Red Sox, fourth-most in club history. Joe Cronin leads with 2,007. … Beltre used some quick footwork at 3B, jumping to avoid a broken bat after firing to second to start a double play on Torii Hunter's grounder in the third. … Boston LHP Alan Embree, designated for assigned on Saturday, cleared waivers and elected for free agency. … The Red Sox honored former SS Nomar Garciaparra with an on-field ceremony before the game. … Scioscia said before the game that Matsui was unlikely to play the outfield for consecutive games. … There was a moment of silence for former Tigers broadcaster Ernie Harwell, who died Tuesday at 92. … Boston RHP Boof Bonser, on the 15-day disabled list with a strained right groin, is scheduled to make his second rehab start with Triple-A Pawtucket Friday at Charlotte. … Youkilis struck out three times.