Dwyane Wade finished with 24 points and eight assists for Miami, which got 18 from Chris Bosh and twice saw its lead cut to three in the final minutes. Cole delivered the answer both times with a pair of jump shots, and the Heat escaped.
Ray Allen scored 28 points on 8 for 12 shooting for the Celtics, while Rajon Rondo finished with 22 points and 12 assists and Keyon Dooling scored 18 off the Boston bench.
Through two games, Miami (2-0) has trailed only once - by two points, for all of 14 seconds.
Cole's jumper with 3:01 left gave Miami a 108-98 lead, most of which disappeared in the next 59 seconds, thanks to Dooling - a former Heat guard. He scored seven straight points, including a 3-pointer with 2:02 remaining, cutting the Heat's lead to three. And when Boston got a stop on the next Miami trip, the Celtics looked for Dooling again.
But Wade stepped in front of a pass intended for Dooling, starting a play where James found Cole for another jumper, and Miami's cushion was back to 110-105 with 1:31 to play.
And with a minute left, it was Cole again, with the biggest shot of the night for Miami. James set him up from the top of the key for another jumper, restoring the five-point edge. When Cole stepped to the foul line to close the scoring, he got "M-V-P" chants from the Miami crowd, something typically reserved for the likes of Wade, James and Bosh.
Boston was again without forward Paul Pierce (bruised right heel), who worked out both Monday and Tuesday and is getting closer to a return. It won't come on Wednesday, however - the Celtics have already ruled him out of that game in New Orleans, but there is some hope of Pierce being in the lineup when Boston makes its home debut against Detroit on Friday.
Predictably, and maybe spurred by the new Eastern Conference championship banner hanging from the rafters, Miami came out flying.
A short bank shot by Wade made it 26-15 at barely the midpoint of the first quarter, setting the tone for an offensive bonanza the likes of which Boston typically doesn't allow. After a late flurry - James setting up Wade for a lob, Wade missing at the rim but James trailing for a tip-in being perhaps the most impressive of Miami's highlight reel to close the second quarter - the Heat took a 69-54 lead into the locker room.
That represented the most first-half points allowed by the Celtics since Feb. 8, 2005, a span of 607 regular-season and playoff games. James and Wade each had 15 points by the break on a combined 9-for-14 shooting and James Jones came off the bench to make all three of his shots, all from 3-point range.
Even when things looked shaky, the Heat got going again quickly.
Allen and Rondo scored the first baskets of the second half, getting Boston within 11. In a flash, Miami's lead was back up to 20 - six straight points by James made it 85-65 midway through the third, and Miami was well on its way to a blowout.
Feasting on Miami's second unit, with James being the only starter on the floor, the Celtics closed the third on an 18-6 run to make it 91-83 entering the fourth. The Heat missed their last eight shots of the quarter - after having missed 14, total, in the first 32 minutes of the game - and Boston capitalized, taking all the momentum into the final 12 minutes.
Even though Miami pushed the lead back to 15 early in the fourth, Boston just kept answering. Rondo spun and flipped the ball to Allen for what became his sixth 3-pointer of the night with 6 minutes left, getting the Celtics to 102-93.
And they kept clawing. So did Cole, and Miami pulled through.
NOTES: After two games, the Heat have 131 points in first halves this season. After three games last season, Miami had 130 first-half points. ... Celtics F Chris Wilcox didn't play in the second half because of a bruised left shoulder. X-rays were negative. ... The Heat said the luster of the matchup wasn't hurt by Pierce not being available. "We play the name on the front of the jersey, not the one on the back," Wade said. ... Celebrity sightings included Miami Dolphins RB Reggie Bush, rapper Rick Ross and retired tennis star Boris Becker
This program aired on December 28, 2011. The audio for this program is not available.