In Boston, Jayson Tatum's 25 points helped the Celtics subdue an injury-hit Cavs line-up to complete a 4-1 win in the best-of-seven series.
The Eastern Conference No.1 seeds will face either the Indiana Pacers or the New York Knicks for a place in the NBA Finals.
But while Boston continued their progress, Oklahoma City's playoff campaign is hanging by a thread after their damaging defeat to Dallas.
Mavericks star Luka Doncic led from the front with a triple-double, finishing with 31 points, 10 rebounds and 11 assists.
The Mavs lead the series 3-2 and can clinch a place in the Western Conference finals with victory in game six back in Dallas on Saturday.
"We just got one more to win out of two games, and that's it," Doncic said. "It's 3-2, but that's nothing. We've got to finish it and go with the same mentality."
Doncic had been furious after the Mavs surrendered the initiative in a game-four loss in Texas on Sunday, but said a more relaxed approach had been the key to Wednesday's commanding effort.
"Sometimes I forget that I love to play basketball, it's the thing I do," Doncic said. "My mental focus was just to go out there with a smile on my face and play basketball."
Doncic was given offensive support from Derrick Jones Jr. with 19 points while three other players made double figures.
Shai Gilgeous-Alexander led the Thunder scorers with 30 points, eight assists and six rebounds.
Cavs injuries take toll
Earlier, Cleveland's hopes of clawing their way back into their series with Boston were rocked before the game after confirmation that three of their top six players -- Donovan Mitchell, Jarrett Allen and Caris LeVert -- were out with injury.
But Cleveland shrugged off that setback to produce a battling performance that saw them get within three points of the Celtics midway through the fourth quarter.
Evan Mobley was superb for Cleveland, pouring in a game-high 33 points while Marcus Morris Sr. added 25 off the bench.
Yet just when Celtics fans at the TD Garden were nervously wondering if a shock defeat was on the cards, Boston stitched together a decisive 13-2 run -- crowned by a three-pointer from Tatum -- that left them ahead by 14 points at 101-87.
Tatum, who also added 10 rebounds and nine assists, said Boston had prepared for a dogfight despite Cleveland's injury-stricken line-up.
"Anybody who's played in this league understands what happens when somebody's best players are out," Tatum said. "The rest of the guys have more freedom, they play with a different level of confidence and they play different.
"Our mindset coming into this game was, 'However long it takes, that's how long it takes'. We didn't expect to win the game in the first or second quarter. We grinded it out."
Tatum said Boston were now determined to snap their dismal recent record in the Eastern Conference finals. Boston have lost in the Eastern Conference finals in four of five appearances since the 2016-2017 season.
"Each year presents different challenges," Tatum said. "Myself and the rest of the crew have been to the conference finals something like four or five times.
"We're battle-tested. We know what it takes. We just have to put the individual things aside and try and get over that hump."
Tatum was one of six Boston players to finish in double figures on Wednesday, with Al Horford adding 22 points and Derrick White 18.
Jrue Holiday finished with 13 points while Jaylen Brown and Payton Pritchard had 11 apiece.
Boston coach Joe Mazzulla paid tribute to the contribution of Horford, who steadied the Celtics down the stretch to close out the win.
"Tonight you saw his gift, his gift is just passion, inspiration, toughness, competitive nature," Mazzulla said.
