"Jay made a great throw, and I was able to go up and get it. After that, I went unconscious," Miller said of his game-winning catch with 3:19 left.
"It was one of those things where instincts kind of take over. I really didn't have time to go up with two, because he put some juice on it. I went with one and, thankfully, pulled it down."
Miller's touchdown reception and a 2-point conversion run by rookie Jeremy Langford, subbing for the injured Matt Forte, gave the Bears (3-5) their first lead of the night. Chicago's past five games, including consecutive losses to Minnesota and Detroit before the trip to San Diego, have been decided by three points or fewer.
Cutler, who had an interception returned for a touchdown and lost a fumble, kept attacking San Diego's depleted secondary and completed 27 of 40 passes for 345 yards.
"We have got to figure out how to win in the fourth quarter," Cutler said. "We have talked about it. We've won games in the fourth quarter, we've lost in the fourth quarter. That's what the NFL is about. You have to play your best in the fourth quarter, and that's what coach [John] Fox has talked about. It's good that it happened today, but we have to continue it."
Cutler calmly led the Bears on the winning 10-play, 80-yard drive after the Chargers opened a 19-14 lead on rookie Josh Lambo's 22-yard field goal. Two plays before the TD throw to Miller, Cutler was hit but still completed a 12-yard pass to Alshon Jeffery on third-and-6.
"The safety flew over the top, and it was just a matter of waiting for Zach to get past the linebacker," Cutler said. "I left it high on him, and he made a heckuva catch. It couldn't have happened to a better guy. For him to come up with a catch, it was something special."
The Bears scored 15 points in the fourth quarter.
Cutler's two TD passes broke the franchise record and gave him 139 with the Bears. He had been tied with Hall of Famer Sid Luckman.
San Diego (2-7) lost its fifth straight game for its longest skid since six straight in 2011. It's the longest losing streak in coach Mike McCoy's three seasons with the Chargers.
Philip Rivers was 26-of-42 for 280 yards. It was the first time in six games that he didn't throw more than 300 yards.
"When you lose five in a row, it's pretty sickening," Rivers said. "When it's like this, you kind of want to dig a hole and hide for a little while."
The Chargers made numerous mistakes.
Rivers threw an 8-yard touchdown pass to Antonio Gates in the fourth quarter, but it was nullified when right guard D.J. Fluker was whistled for being an ineligible receiver downfield. The Chargers had to settle for Lambo's 22-yard field goal.
Earlier on that drive, wide receiver Stevie Johnson spiked the ball after making a catch for a first down at the 4 and was whistled for delay of game.
"It's all emotion. We're out there playing hard, and I was trying to get in the end zone," Johnson said. "I didn't really spike it that hard, but they called it, and that is part of it. I've got to be smarter than that."
The Bears had a rough first half, but the Chargers couldn't put them away.
Cutler lost a fumble on a sack and then made an off-the-mark throw to Jeffery, which second-year cornerback Jason Verrett intercepted and returned 68 yards for a 13-0 lead.
The Chargers suffered more injuries. Verrett hurt his groin one play after his pick-six and came out but remained on the sideline. Cornerback Patrick Robinson left with a neck injury.
Wide receiver Malcom Floyd, playing his final NFL season, injured his left shoulder while diving to make a catch. Eight days earlier, San Diego's Keenan Allen, one of the NFL's leading receivers, suffered a season-ending lacerated kidney when he landed hard at the end of a spectacular touchdown catch in a loss at Baltimore.
Cutler broke the franchise record for touchdown passes when he found Martellus Bennett for a 1-yard score midway through the second quarter.
Cutler had been tied with Luckman with 137 touchdown passes with the Bears. Cutler began his career with the Broncos. Luckman threw his final touchdown pass as a member of the Bears on Sept. 17, 1950.
Langford scored on a 1-yard run early in the fourth quarter to start Chicago's comeback.
McCoy fell to 20-21 in three seasons. ... Fox, who was McCoy's boss at Carolina and Denver, improved to 5-1 against McCoy.
Orlovsky: The Ravens have one of the NFL's sloppiest pass offenses
Dan Orlovsky and Ryan Clark break down the offensive woes for Lamar Jackson and the Ravens.
Why Stephen A. has the Packers as the NFL's most complete team
Stephen A. Smith details why Aaron Rodgers and the Packers are the most complete team in the NFL.
How the Pats' MNF win drastically altered the AFC picture
Seth Walder explains how the Patriots' win over the Bills affected the AFC picture and reveals the intriguing matchup which is most likely in the Super Bowl.
Baby Stephen A. makes a case for the Cowboys
Baby Stephen A. questions Stephen A. Smith not including the Cowboys on his A-list.
Cleveland Browns place tight end David Njoku on COVID-19 list
Browns tight end David Njoku was placed on the reserve/COVID-19 list Tuesday.
Ben Roethlisberger, Pittsburgh Steelers balancing recovery, preparation during short week
Ben Roethlisberger isn't a fan of short weeks, especially after physical games, but he said he and his teammates will deal with their aches and pains by balancing recovery and preparation ahead of Thursday's game vs. the Vikings.