Allen made a tiebreaking 3-pointer with 2 seconds left and finished with 30 points, leading the Celtics to a 118-115 win over the Chicago Bulls.
Gordon nearly carried Chicago to a 2-0 lead in the best-of-seven series. He scored with 12.3 seconds left to tie it, the final hoop of his playoff career-high 42 points. Then Boston set up a play for Allen, who took a pass from Rajon Rondo and connected from the right side.
Allen scored 28 points after getting some advice from coach Doc Rivers at halftime.
"Doc said going into the half, 'Be aggressive, but let it come to you,'" Allen said. "I never think I'm not in my rhythm. It can be a grind as a shooter. As a scorer you're always trying to find something."
Allen and Gordon each had several clutch baskets in the second half as the former University of Connecticut guards battled for control of the game. After Tyrus Thomas missed a shot from midcourt as time expired, Allen headed for his bench where injured Kevin Garnett delivered a couple of congratulatory slaps -- to his head and chest.
Allen said he doesn't like "being made a fuss over." But that was unavoidable after he broke out of his shooting slump. He scored just four points on 1-for-12 shooting and missed the final shot in Chicago's 105-103 overtime win Saturday.
"It felt like we were at UConn in the summertime playing pickup," Gordon said. "He is a great shooter and I knew he would break out eventually."
The next two games of the series are scheduled for Chicago on Thursday night and Sunday.
"We feel very confident because we feel like we haven't even played good basketball yet," Boston's Paul Pierce said. "Our best is yet to come."
The Bulls showed they could compete with the Celtics, who could be without Garnett (strained right knee) for the rest of the playoffs.
"We got a split and that's tough to do against the defending champs," Gordon said.
Consecutive 3-pointers by Gordon gave the Bulls a 109-104 lead before the Celtics rallied. Glen Davis made two free throws and Rondo connected on a long jumper to give Boston a 112-111 lead with 1:01 to play.
Gordon followed with a 16-foot jumper and Allen countered with a 3-pointer that put Boston ahead 115-113 with 25.3 seconds remaining.
Then it was Gordon's turn. He connected from near the foul line before the Celtics called a timeout to set up their final play.
Rondo dribbled on the left side and Allen worked himself free, caught the pass in rhythm and converted as the crowd went wild.
On his way to the locker room after Thomas missed the last shot for Chicago, Rivers shouted, "yeah, yeah," pumped his fist and exchanged high-fives with fans. Then, headed to his postgame news conference, Rivers joked, "nice and easy, never a doubt."
Davis had 26 points for second-seeded Boston, passing his career high of 24 points on March 21, and Rondo had a triple-double -- 19 points, 16 assists and 12 rebounds. Pierce added 18 points and Kendrick Perkins contributed 16 points and 12 rebounds.
The Allen-Gordon shootout "almost looked like they turned it into a personal battle," Rivers said. "You know, who's the best UConn player to ever play. And it was amazing."
"We were exchanging jabs there, and I don't mean shots," Allen said. "I mean he caught me with an elbow, I got him right back with an elbow. It was ... competitive."
Chicago coach Vinny Del Negro cited the Celtics' rebounding as a key to their win.
"They had 21 offensive rebounds," he said, "and it's going to be hard to win any game, not even a playoff game, if you give up that many offensive rebounds."
The Celtics nearly lost despite controlling rookie point guard Derrick Rose, who sat out most of the first quarter with two fouls. He finished with 10 points, seven assists and six rebounds after leading the Bulls with 36 points and 11 assists on Saturday.
Rondo missed the last 5:03 of the first half with a minor right ankle sprain but returned to start the third quarter. Backup forward Leon Powe didn't return to the bench after going to the locker room early in the second quarter. Rivers said he didn't know anything about Powe's condition "but it didn't look good."
According to ESPN's Wendi Nix, Powe was sent to Massachusetts General Hospital to undergo an MRI on his left knee. Powe had previously been suffering from a right knee sprain.
Garnett spent the entire game on the bench, mostly standing. In the opener, he was there for the first half but stayed in the locker room after intermission. ... Gordon's previous playoff high was 35 points. ... The game was played on the 23rd anniversary of Michael Jordan's NBA playoff record of 63 points. Boston beat Chicago 135-131 in double overtime. ... Red Sox pitchers Josh Beckett, Jon Lester and Justin Masterson attended the game. Masterson was the winning pitcher in a 12-1 victory over Baltimore on Monday, allowing one run in 5 1/3 innings. ... Boston Celtics owner Wyc Grousbeck was at the game after finishing the Boston Marathon earlier Monday in 4:16:49. He sat next to New England Patriots owner Robert Kraft.
Information from The Associated Press was used in this report.