The Toronto Raptors more than did their part, too.
Outlaw scored the final eight points for New Jersey in a 137-136 triple overtime win Saturday night that gave the Nets a sweep of their two games in London.
The game featured four missed buzzer-beaters and provided exactly the kind of thrilling finish league officials were looking for when they decided to bring regular-season games to Europe for the first time.
Outlaw made two free throws with 12.6 seconds remaining to put the Nets ahead for good and Andrea Bargnani missed a jumper at the buzzer as New Jersey swept the doubleheader at London's O2 Arena.
"Hats off to the NBA ... because I think it's a huge success," Nets coach Avery Johnson said of the European experiment. "This is one of the best wins I've been a part of."
Brook Lopez had 34 points and 14 rebounds for the Nets but fouled out in the second overtime.
Deron Williams added 21 points and 18 assists for his fifth straight double-double since joining the Nets from Utah last week.
DeMar DeRozan finished with 30 points for Toronto (17-46) for the second straight night.
Bargnani led all scorers with 35 points, but also missed a potential winner with 2 seconds left in the first OT.
"We had more than one opportunity to win the game," Bargnani said. "It's been an unbelievable game. Unfortunately we lost."
New Jersey won the first game at the O2 Arena in London 116-103 on Friday.
Williams, who missed a shot to win it at the end of regulation, made a jumper with 9.8 seconds left in the second overtime to tie it at 126, and DeRozan's shot at the other end then clanked off the rim with 2 seconds left. Bargnani grabbed the rebound but couldn't get a shot off before the buzzer.
Vujacic then made 3 free throws to start the third OT, before Outlaw took over the game at both ends.
After making two more free throws, Outlaw blocked Bargnani on the next possession and held on for a jump ball against Amir Johnson. The ball went to Vujacic who missed an easy layup, but Jordan Farmar ended up with the rebound and found Outlaw for a long jumper.
On New Jersey's next possession, Outlaw grabbed his own rebound for a putback to make it 135-128.
"He was instrumental in our win today," Williams said. "We thought we had a mismatch with him on the offensive end. He stepped up and made some big shots but also made some key defensive plays on the other end."
But Toronto responded with eight straight points, capped by Leandro Barbosa's 3-pointer with 21 seconds left, only for Johnson to foul Outlaw while shooting a jumper on the next possession.
The forward made both shots, and Bargnani's long jumper rimmed out at the buzzer.
"Take your hat off to Toronto, they deserved to win just as much as we did," Johnson said. "Unfortunately, these games don't finish in a tie."
Perhaps some British fans thought it did. A few hundred left the arena between the end of regulation and the third overtime period -- although it was more likely to make sure of making the last underground train home.
The Nets were up 65-62 after a first half that featured a crowd-pleasing run-and-gun style of play but little defense from either team. The Nets shot 56.5 percent from the field in the first two quarters -- compared to 55.6 percent from the free throw line, where they made 5-of-9.
Williams finished the half one assist shy of a double-double.
DeRozan has made his past 34 free throw attempts after going 6-for-6 on Saturday ... Sports celebrities in the crowd included Arsenal players Cesc Fabregas and Samir Nasri along with Chelsea players Branislav Ivanovic and Petr Cech.