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 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.
Cardinals at Dodgers
P Monday, 6:07 p.m.
TV • TBS
All games on Ch. 13
Saturday • Detroit 1, Boston 0
Sunday • Boston 6, Detroit 5
Tuesday • Boston (Lackey 10-13) at Detroit (Verlander 13-12), 2:07 p.m.
Wednesday • Boston (Peavy 12-5) at Detroit (Fister 14-9), 6:07 p.m.
x-Thursday • Boston at Detroit, 6:07 p.m.
x-Oct. 19 • Detroit at Boston, 2:37 p.m.
x-Oct. 20 • Detroit at Boston, 6:07 p.m.