Dinwiddie's 25-foot winner sealed a pulsating tussle in Brooklyn which had been dominated by a thrilling duel between Nets star Kevin Durant and the Mavericks' Luka Doncic.
Durant looked to have edged the Nets into a game-winning position with 10 seconds remaining after sinking a three-pointer from 27 feet to put Brooklyn 111-110 ahead, just after Doncic's fadeaway jumper gave Dallas a slender 110-108 lead.
But with the last play of the game, Doncic worked the ball to Dinwiddie on the edge of the arc and the shooting guard made no mistake with the three for a 113-111 victory.
It capped a superb fourth-quarter performance from Dinwiddie, who scored 15 of his 22 points in the final period.
Dinwiddie, who joined Dallas in a trade from the Washington Wizards last month, insisted Doncic, who finished with 37 points with nine rebounds and nine assists, should take the credit.
"That was Luka making a play rather than me doing anything special," Dinwiddie said.
Brooklyn looked to have taken a decisive advantage after leading 91-79 at the end of the third quarter in front of a sellout 17,981 crowd at Brooklyn's Barclays Center arena.
But Dinwiddie's late burst of scoring helped the Mavs outscore the hosts 34-20 in the final period to seal victory.
Durant led the Nets scoring with 23 points, while Goran Dragic added 21.
The Mavericks improved to 43-26 with the win to remain fourth in the Western Conference while the Nets fell to 36-34 in the East.
In other games, the Golden State Warriors were given an injury scare after Steph Curry limped out of their 110-88 home defeat to the Boston Celtics in San Francisco.
Curry hobbled back to the locker room in the first half with a sore foot after the Celtics' Marcus Smart dived into the Warriors star's left ankle.
Curry did not return and the Celtics pulled clear for a convincing win, with Jayson Tatum and Jaylen Brown each contributing 26 points.
In Sacramento, Giannis Antetokounmpo finished with 36 points to help the Milwaukee Bucks overcome a spirited Kings side.
A neck-and-neck encounter went down to the final few minutes before the Bucks pulled clear thanks to a combined 27 points in the final quarter from Antetokounmpo, Khris Middleton and Jrue Holiday.
In Cleveland, Joel Embiid celebrated his 28th birthday with a 35-point display as the Philadelphia 76ers held on for a 118-114 win over the Cavaliers.
The Sixers looked to be cruising after a dominant first half which included a 42-point second quarter to put them 72-59 ahead at the break.
But an improved Cavaliers defensive display stifled the Sixers' scoring in the third period as the home side outscored the visitors 31-13 to lead by five heading into the final quarter.
Philadelphia took control in the fourth quarter however, with Embiid, James Harden and Tyrese Maxey combining for 25 points to shepherd the Sixers over the line.
Embiid finished with 35 points, 17 rebounds and five assists, with support from Maxey (25 points), Harden (21) and Tobias Harris (19).
Suns thrash Rockets
Embiid was in anything but a celebratory mood however after a game which saw the Sixers almost squander a 17-point lead.
"Obviously we made the right plays at the end, but we can't keep blowing these leads," Embiid said.
"We've got to do a better job, especially when we get these leads --staying focused, getting stops, and moving the ball on offense."
In other games, Devin Booker scored 36 points to inspire the Western Conference-leading Phoenix Suns to a blowout 129-112 win over Houston.
In Washington, Nikola Jokic scored 29 points in the Denver Nuggets' 127-109 win over the Wizards.
In Minnesota, Karl Anthony-Towns followed up Monday's 60-point masterclass with 30 points as the Timberwolves romped past the struggling Los Angeles Lakers 124-104.
The Lakers were never in contention as Minnesota led from start to finish, outscoring the visitors 31-17 in the first quarter alone.