Now the Celtics look to make up some ground on the team directly ahead of them in the Eastern Conference standings as they try to extend the Atlanta Hawks' woes in Boston on Friday night.
With 2.1 seconds left, Green drove to the basket and would score the game-winner at the horn as Boston (37-34) snapped a five-game losing streak with a 93-92 win at Cleveland on Wednesday.
Green, getting major minutes with Kevin Garnett out of the lineup, finished with 21 points and seven rebounds. He's averaging 21.4 points on 52.6 percent shooting - including 12 for 23 from 3-point range - in seven starts this season.
"Now we have another guy that's gaining confidence at the end of games and knows that he can get it done," said Paul Pierce, who added 19 points and 10 rebounds.
Green is likely to continue starting in place of Garnett, who has missed the last three games and five of seven with inflammation in his left ankle. He's expected to be out until at least next week.
The Celtics stormed back from a 14-point fourth-quarter deficit against the Cavaliers to avoid equaling the season-high six-game skid they suffered Jan. 16-25.
"It was a huge win," Pierce said. "We didn't play well from the second quarter on, but we found a way. It seemed like we were mentally fatigued and physically fatigued, but we put it all together at the end."
Now the Celtics have an opportunity to pick up a full game on the Hawks, who lead Boston by 2 1/2 games for sixth place in the East.
While the Celtics aren't completely out of the chase for home-court advantage in the first round, the Hawks (40-32) have a much better shot at it. They're in a virtual tie with Chicago for the fifth seed and trail fourth-place Brooklyn by 2 1/2 games.
Atlanta secured a playoff berth for a sixth straight season with a 107-88 victory at Toronto on Wednesday.
"We just want to be in the best position that we can, whatever that is," said Horford, who has totaled 46 points and 26 rebounds in the last two meetings with the Celtics.
Both of those games went past regulation. The Hawks overcame a 27-point deficit to win 123-111 in double-overtime Jan. 25, and they rallied from 12 down in the fourth quarter at Boston on March 8 only to lose 107-102 in overtime.
That was the Hawks' sixth consecutive road loss in the series, though three of those games went to overtime. They have dropped 15 of 17 in Boston, including the 2008 and 2012 playoffs.
Boston leads this season's series 2-1, with Pierce averaging 26.5 points in the two wins and getting held to 12 on 4-of-13 shooting in the loss.
Teague has averaged 22.0 points on 55.6 percent shooting in the three meetings.
Celtics guard Courtney Lee will be a game-time decision after sitting out the last three games because of a sprained left ankle.