The Cavs will attempt to win their third consecutive Eastern Conference title and trip to the NBA Finals while it would be the seventh in as many years for LeBron James should Cleveland prevail.
Unlike numerous previous games in this series, it was the Celtics who jumped out to the early advantage, leading 10-2 after the first few minutes.
Boston beat the Washington Wizards 115-105 in Game 7 of the Eastern Conference semifinals Monday night.
For both the Celtics and the Wizards, the next round means a meeting with the defending NBA Champions, the Cleveland Cavaliers, which hasn't gone good for any team to face them in the last two years.
Game 7 was filled with a lot of back-and-forth action, with each team trading the lead throughout the game.
But Washington quickly responded, scoring seven straight in just 51 seconds to get back within six.
With the game tied at 17, rookie Jaylen Brown came off the bench to spark a 7-0, including a 3-pointer and a pair of free throws. Washington did a better job of isolating Thomas in the post, but they didn't punish him enough and nobody besides Beal could hit a shot.
Olynyk's heroics helped the Boston bench outscore the Washington reserves 48-5.
The Wizards were down 3-2 going into Saturday Night's game in Washington. But in the fourth quarter, he was scoreless despite playing all but nine seconds of the quarter.
The Wizards got within four points as Bradley Beal single handily kept them in it with 38 points, but a layup by Olynyk and a one-footer by Thomas (off an Olynyk offensive board) gave Boston a little breathing room. Then Olynyk took over.
This was a worthy Game 7, a tight, well-fought nerve-wracker that could have gone either way.
Aside from fouls, the Celtics especially were troubled in the rebounding department, as the Wizards outrebound the C's 23-14 through two quarters.
In the regular season, the Cavs went 3-1 against the Celtics.
The Boston Celtics' season will continue.
Marcus Smart, Amir Johnson and Olynyk all were whistled for three fouls in the opening 24 minutes, though Smart did inject some life into a second unit that outscored their Wizards' counterparts 19-5.
Olynyk had 14 of his points in the fourth quarter and was the X-factor that swung the series in Boston's favor. After a bad turnover by John Wall, Isaiah Thomas drained a deep straightaway three with exactly 10 minutes left, putting the Celtics ahead, 94-81. The play of Thomas has been inspiring for the past month, even as he has slowed down lately, and big man Al Horford has silenced critics with his all-around game. Much the same is true for Wall, who said he would think of this season as a disappointment if they forced Game 7 only to come up short.