The Tigers were cruising to their second straight win at Fenway Park, with starter Max Scherzer taking a no-hitter and a 5-0 lead into the sixth inning.
But with one swing, Big Papi flipped everything. Ortiz hit a two-out shot that sent right fielder Torii Hunter jack-knifing into the Boston bullpen in a futile attempt to catch the ball, making it 5-up.
Saltalamacchia's single came after a series of Tigers misplays in the ninth. A wild throw, a wild pitch and a missed catch by first baseman Prince Fielder on a foul ball set up the game-ending hit.
The teams head to Detroit for Game 3 on Tuesday. Justin Verlander will face Boston's John Lackey.
Boston's big comeback followed a dramatic New England Patriots' victory right down the road in which Tom Brady threw the game-winning touchdown pass with 5 seconds left to beat New Orleans. The score was greeted with cheers by Red Sox fans waiting for the baseball game to start.
A day after Anibal Sanchez and the Detroit staff combined on a one-hitter for a 1-0 win, Scherzer excelled. He fanned 13 while allowing two hits in seven innings, and was pulled after 108 pitches.
"It's playoff baseball," Tigers manager Jim Leyland said. "Looked like we had one in hand and we let one get away, there's no question about that. But there have been two great games."
Miguel Cabrera and Alex Avila homered off Clay Buchholz in Detroit's four-run sixth inning.
Boston scored once in the bottom of the sixth and then loaded the bases against three relievers in the eighth before closer Joaquin Benoit came in to face Ortiz.
On his first pitch, Ortiz hit a line drive into the glove of the Red Sox bullpen catcher, with Hunter flopping headfirst over the chest-high wall in pursuit.
The fans waited until the trainers verified that Hunter was OK to start chanting, "Papi!" and call the Red Sox slugger out of the dugout for a curtain call.
It was the first career postseason grand slam for Ortiz, a star of the 2004 playoff run that ended in Boston's first World Series title in 86 years.
"When you consider down four runs, not a very likely scenario that you come back from that many runs that late in the game," Red Sox manager John Farrell said.
Koji Uehara pitched a perfect ninth for the win. Rick Porcello took the loss.
Jonny Gomes led off the bottom half against Porcello with groundball to the left of shortstop Jose Iglesias, a defensive replacement. The former Red Sox prospect fielded it but rushed the throw and it bounced past Fielder and into the Boston dugout as Gomes slid headfirst into the bag with an infield hit.
With Gomes on second because of the error, Saltalamacchia hit a high popup near the rolled-up tarp that bounced off Fielder's glove.
A fan reached up trying to catch the foul. Fielder looked as if he wanted an interference call — replays showed he simply let the ball glance off his glove.
Gomes took third on Porcello's wild pitch and Saltalamacchia hit a sharp grounder through the left side of the drawn-in infield to set off a celebration on the Fenway infield.
Scherzer, who led the majors with 21 wins, struck out 13 and did not allow a hit until Shane Victorino singled to left with two outs in the sixth.
It was an unprecedented third consecutive playoff game in which a Tigers starter took a no-hit bid into the sixth inning. That had never been done even twice in a row before this year's Detroit staff, which boasts the AL ERA leader, the major league leader in wins and the 2011 AL Cy Young winner and MVP.
In his first career ALCS start, Buchholz allowed five runs on eight hits in 5 2-3 innings while striking out six.
One night after Jon Lester absorbed a 1-0 loss, Buchholz kept the Red Sox in the game despite allowing three straight hits in the second and spotting Detroit to a 1-0 lead.
But Cabrera hit a solo shot off the light tower above the Green Monster in the sixth, then Fielder lined a double off the left-field wall. Victor Martinez followed with an RBI double to right-center and Avila hit a two-run shot over the Tigers bullpen to make it 5-0.
Scherzer continued to coast, striking out at least one batter in every inning. The favorite for the AL Cy Young Award after going 21-3 with a 2.90 ERA in the regular season, Scherzer allowed one run on two hits and two walks before leaving after seven innings with a 5-1 lead.
NOTES: Dave Roberts, whose stolen base sparked Boston's comeback in the 2004 ALCS against the New York Yankees, threw out the ceremonial first pitch. ... Ortiz's 63rd postseason game tied Jason Varitek for the Red Sox franchise record. ... Buchholz had a 1.20 ERA against the Tigers in four career starts at Fenway Park. ... Victorino's nine career hit by pitches in the postseason tie him with Alex Rodriguez for the major league record. .. Scherzer lost 2-1 at Fenway Park on Sept. 9 when going for his 20th win.
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