Head coach Rudi Garcia lavished praise on his resilient Roma team after the capital club set a new record for the start of a Serie A season.
Despite the Giallorossi losing Maicon to a red card in the second half of Sunday's match at the Stadio Friuli, where Udinese had not lost since September 2012, American midfielder Michael Bradley scored from the bench to decide a 1-0 victory - a ninth win on the spin for Roma.
Fabio Capello's Juventus achieved the same feat at the start of the 2005-06 season but the Turin club's record was expunged as a result of the 'Calciopoli' match-fixing scandal which saw stripped of two titles and forcibly relegated to Serie B.
Roma are now five points clear of Juve and Napoli ahead of Thursday's visit of bottom side Chievo to the Stadio Olimpico.
French coach Garcia told asroma.it: "This win was our best one yet.
"We played with our heads and our hearts, which is what we've been doing since the beginning of the season.
"To win with 10 men at the Stadio Friuli, where Udinese hadn't lost in over a year, is something very important for our future. And at the end of the season it's certainly going to count.
"The build-up to the goal was fantastic because we only had 10 players on the field. This team believes in itself and has the power to attack even when it's outnumbered.
"Even when we were down a man we played to win, which was great."
The former Lille boss will not, however, be encouraging his players to get themselves dismissed in a bid to spark similar late rallies.
"Is it true you play better and play to win when you're down to 10 players? Maybe in just a one-off situation, but not in every game," he said, laughing.
"You create your own luck. It doesn't come by itself. Let's not forget that we were playing outnumbered at the end of the game.
"The most important thing is to believe in the strength of the team and to have confidence in your team-mates and the group as a whole."
Udinese coach Francesco Guidolin, whose watched his team lose for the fifth time this season, bemoaned his players' failure to exploit their one-man advantage.
Antonio Di Natale and Luis Muriel did go close to scoring while Gabriel Silva had a goalbound effort cleared off the line by Leandro Castan.
"Roma are very healthy at the moment, and have proved to be a very good team," Guidolin said. "They were good at absorbing the dismissal and were quite lucky in the first half.
"But we should have tried to beat them when their man was dismissed.
"I just think we haven't had the right chance to score. Unfortunately we haven't taken any points, but we've done our best.
"Our future performances must be like today's or better, we must improve."