The only problem? He hasn't pitched for them in two years.
"David, he's as big time of a player of anybody I've ever played with," Peavy said after giving up four runs on three hits and a walk with six strikeouts over six innings.
"He's a special type talent that just -- when he's gone, the game will have a huge void in it that I don't know who's walking into those shoes."
"Peavy's always going to be remembered here and welcomed to Boston," Ortiz added. "Great teammate and great personality. I really enjoyed being his teammate."
Peavy (5-8) was a part of the Red Sox's 2013 World Series championship team before Boston traded him to San Francisco a year later. He received a standing ovation from the Fenway faithful during warm-ups in the second inning.
"That was awesome," Peavy said. "I love Fenway Park and getting a chance to come back here as a visitor.
"Tonight was different because you're in compete mode and you're trying to find a way to win, but I certainly appreciate the fan response."
In fact, he enjoyed his time with the Red Sox so much that he bought the duck boat he and his teammates rode during the team's championship celebration in 2013.
"I own a duck boat that's beautifully painted now in Red Sox colors," Peavy said. "My family and teammates hanging off the side of it on parade day, Boston means the world to me."
Ortiz's homer was No. 526 of his career, bringing him within eight of Jimmie Foxx for 18th place on the all-time list. It was the 40-year-old slugger's 994th extra-base hit with the Red Sox.
Brock Holt added a solo homer for Boston, which is a season-high-tying 13 games above .500. The Red Sox (52-39) won their fifth consecutive home game and improved to 10-3 in the month of July.
"Just want to keep on winning and keep on providing things to win ballgames," Ortiz said. "That's all that matters."
San Francisco (57-37) entered the night with the best record in the majors, but it endured its fourth defeat in a row after a surprising three-game sweep at San Diego over the weekend.
"We look flat right now," Giants manager Bruce Bochy said. "You look flat when you don't hit or drive in a run, and they start pressing a little bit and we've got to get on track here soon."
The Giants have not won a game at Fenway in four tries since moving to San Francisco in 1958. San Francisco was swept by Boston in a three-game series at Fenway from June 15-17, 2007.
Red Sox starter Rick Porcello (12-2) moved to 9-0 at home this season, tossing 6 1/3 scoreless frames while allowing four hits and two walks and striking out three.
"I think more than anything Rick is just in a very comfortable place in this ballpark," Red Sox manager John Farrell said.
Boston is 10-0 in Porcello's home starts this season.
Koji Uehara, pitching in a non-save situation in the ninth, departed after recording a strikeout on just seven pitches. Tommy Layne, the fourth reliever to follow Porcello, entered and sealed Boston's victory.
"Little bit of a pec strain," Farrell said of Uehara. "Had to get him out of the ballgame."
Peavy breezed through Boston's first eight batters until Holt unloaded on a 3-2 fastball for a homer to center in the third.
Ortiz followed suit in the fourth, blasting Peavy's offering an estimated 436 feet and well past the bullpens in right for his three-run bomb.
NOTES: San Francisco signed RHP Kyle Drabek to a minor league contract. "At our request, (he) is taking ground balls and giving us a look at him as an infielder ... but we're not ruling out his continuing with us from the mound," Giants GM Bobby Evans told ESPN. ... Giants RF Hunter Pence (right hamstring strain) was held out of a rehab game with Triple-A Sacramento on Tuesday. "(The trainers) thought it's wise to give him one more day," Giants manager Bruce Bochy said, adding that 2B Joe Panik (concussion) played five innings. ... The Red Sox held a moment of silence and unity before the game. The words "We Are One" were displayed on the video board as the teams were joined on the field by police officers. "Let's be kind to each other, and choose love," Boston DH David Ortiz said to the crowd. ... Red Sox RHP Junichi Tazawa (right shoulder impingement) threw all of his pitches during Tuesday's simulated game and is likely to return Friday. ... Bochy walked Boston's iconic Freedom Trail on the off day Monday. ... New England Patriots star Rob Gronkowski threw a ceremonial first pitch to Ortiz. ... Giants RHP Matt Cain (1-5) opposes LHP Drew Pomeranz (8-7) on Wednesday.