The Mavericks lead the West Conference finals series 3-1 and can secure a place in the championship game against the Miami Heat or the Chicago Bulls, with a victory in game five in Dallas Wednesday.
Dallas had not lead at any stage in regulation and were 15 points down with just over four and a half minutes remaining in the fourth quarter before the game ended in a dramatic turnaround.
"One thing about this team all year, they've been resourceful, they keep on believing, and we've been extremely opportunistic. The way they hung in tonight was just fantastic," Mavericks coach Rick Carlisle said.
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While Dallas never lost faith in their ability to comeback, the Thunder looked a different side completely on offense after the influential James Harden fouled out with 4:34 remaining.
Dallas then finished with a 17-2 run with the magnificent Nowitzki producing two free throws in the final seven seconds as the game was tied at 101-101 after regulation.
In overtime Dallas took control over a demoralized Thunder, a three pointer from the excellent Jason Kid, with 40 seconds left on the clock, proving decisive.
The Thunder, who only came into existence in 2008 after the Seattle SuperSonics moved to Oklahoma City, looked dejected during time-outs in the latter stages - their body language betraying the shell-shocked state of a youthful team.
"Our youth is not an excuse," said Thunder top scorer Kevin Durant, who made 29 points but also had nine of Oklahoma City's 25 turnovers.
"We just weren't making shots and they were. I feel upset because I feel I let the fans down, let the city down. We have to come back and push hard and try to bring it back to OKC," he added.
Nowitzki's 40 point performance was his second in this series and included 14 on 15 free throws and some outstanding turnaround jump shots.
Durant and the Thunder started with impressive intensity and led 31-22 after the first quarter but Dallas fought back with the seven-foot tall Nowitzki making 17 points in the second quarter.
"We kept believing, we got some rebounds at last, that had been killing us. We got some great stops in the last couple of minutes. We are happy with this win but it's not over yet," said Nowitzki.
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