They presumably didn't want to make a mess of the court where he was essentially a coach between the lines for the Mavericks when they won the franchise's only title in 2011.
Joe Johnson scored 22 points, including the tying layup in regulation and the go-ahead 3-pointer in overtime, to lead the Nets past the Mavericks 107-104 Sunday night in Kidd's first game as a coach in the city where his career started in 1994 and reached its peak in his second stint 17 years later.
The Nets swept the two-game season series with Dallas in their first year under Kidd, who was also celebrating his 41st birthday.
''It's a little wet in there,'' Kidd said, warning of the pile of ice surrounded by towels in the middle of the locker room floor. ''You guys be careful. I don't want any media getting hurt.''
Marcus Thornton had 11 of his 20 points in the fourth quarter for the Nets, who won their fourth straight game and beat a Western Conference team for the fifth straight time.
Nowitzki hit his first shot of overtime after going 1-of-10 in regulation, but the Mavericks couldn't make any shots until it was too late in overtime.
Nowitzki was 2-of-12 from the field, finishing below 42 percent for the third time in four games as the Mavericks dropped to 2-2 on a franchise-record eight-game homestand.
Both losses have been in overtime, and now Dallas faces back-to-back games against teams with much more secure playoff futures in Oklahoma City and the Los Angeles Clippers.
''This is not the time to panic,'' said Ellis, who had four assists and four turnovers. ''We still have four more home games. We are going to try to get these four.''
After a layup that tied the score with 9 seconds left in regulation, Johnson put the Nets up 96-93 early in overtime with a 3-pointer and answered a pair of free throws from Nowitzki with a jumper.
After another miss by Nowitzki, Shaun Livingston stepped in front of a pass from Shawn Marion and went the distance for a layup and Brooklyn's biggest lead at 100-95.
Deron Williams and Paul Pierce had 15 points apiece for the Nets.
The Mavericks, who led by 14 points after the first quarter and midway through the third, were up four with 44 seconds left in the regulation when Pierce hit two free throws after getting fouled by Marion.
After Nowitzki shot an airball on a fadeway, Johnson drove for a layup and a 91-all tie. Ellis missed a long 3-pointer at the buzzer in regulation.
Sam Dalembert had season highs of 15 rebounds and seven blocks, and he had two huge plays that weren't rebounds when he was fouled trying to get the ball and made three of four free throws in the last 1:11. Dalembert scored 12 points.
The Mavericks led by 14 after the first quarter and again midway through the third before the Nets made a charge with a 14-0 run to a 73-72 lead on two free throws from Williams. Thornton had consecutive 3-pointers to get Brooklyn within a point.
''We just had too many lapses tonight,'' Dallas coach Rick Carlisle said. ''A lot of them were on innocent plays when we had a lead, but, you know, in a one-possession game, those things come back to you.''
Devin Harris, who was traded to the Nets when Kidd returned to Dallas in 2008, came off the bench much earlier than usual after Jose Calderon was knocked out of the game just 45 seconds in by an inadvertent elbow to the face from Mason Plumlee.
Calderon didn't return, and Carlisle said his status is uncertain.
Harris hit three 3-pointers in the first 6 minutes and led the Mavericks with nine points in the first half. He finished with 11 points, seven rebounds and six assists in a season-high 40 minutes.
NOTES: Nets F Andrei Kirilenko left in the first half with a mild left ankle sprain and didn't return. ... The Mavericks showed a clever ''Shawn Marion training video'' making light of an unconventional shooting style where he short-arms the ball with his right hand. Marion was laughing when he came off the bench after the timeout. ... Nets F Mirza Teletovic had nine points after getting a career-high 34 in 107-106 win at Brooklyn in late January.