Green shot with 100 per cent accuracy on his way to posting a season-high tally of 16 points from the bench.
Green imposed himself on the defensive end as well, setting a screen on Kevin Durant that was so effective it coaxed the Nets star into lashing out and conceding a technical foul.
Green is shooting the three ball at better than 61 per cent this season and remained on court as Dallas pulled off a late 14-0 run.
But Brooklyn rallied and, down 96-93, had a chance to send the game to overtime when Durant stepped to the stripe for three shots in the final nine seconds.
He was on a streak of 62 successful free-throws but missed his second attempt to hand the Mavs a pulsating win.
"We've had too many (crazy finishes) already in the season," Green said post-game.
"It's a good learning stage for me being a part of the game at the end. We stuck with it, we had a game plan.
"We made a couple of mistakes that they took advantage of but we came out with the win and that's what matters."
Starting from the bench for the first time in his career, Simmons switched to centre on his return from knee soreness but again struggled to find his mojo.
Coming on for Nic Claxton late in the first quarter, the switch took some of the pressure off Simmons to shoot the ball, a well-documented weakness, but his inexperience setting screens was evident.
The former No.1 draft pick finished with a meagre stat line: two points, three rebounds and two assists from 16 minutes on the floor.
Elsewhere, the Hawks halted Milwaukee's unbeaten start to the season with a big 117-98 win in Atlanta.
The young Australian couldn't find his rhythm early - the Thunder were +8 without him and -3 with him in the opening quarter - but acclimatised to the contest after the first change.
Giddey joined forces with Tre Mann to help Oklahoma City open up a 16-point lead but after a foul and a turnover to start the final quarter, Giddey was benched in favour of Lu Dort and the Pistons broke away.
Still without former league MVP James Harden (foot), the Sixers led from the fifth minute of the first quarter and never surrendered their advantage.