A burst of three goals in seven first-half minutes - Goran Pandev netted twice before Federico Fernandez scored an own goal - gave fans at the Stadio San Paolo a taste of things to come.
Napoli, who would have joined Roma on 34 points with victory, recovered immediately from Bruno Fernandes' equaliser through Blerim Dzemaili, but Basta had the last laugh with a leveller 10 minutes from time.
The Azzurri remain in third place while Udinese move up to 12th having clinched their first point on the road since October.
Lorenzo Insigne was a constant menace to Udinese in the early exchanges and soon dribbled past Basta to slide a cross into the box, where Allan cleared his lines.
Home debutant Rafael Cabral made a firm save from Fernandes before Insigne raced up the other end to feed Raul Albiol for a header, which bounced just wide of a post.
The end-to-end action continued and, after Rafael had blocked Roberto Pereyra's bullet header, the opening goal arrived in the 38th minute.
Fernandez looped a corner into the Udinese box and Pandev was Johnny-on-the-spot, spinning and tucking home from six yards.
Three minutes later, the Macedonian scored again.
This time Gonzalo Higuain did all the hard work, bursting into the area with tremendous speed before centreing to Pandev, who controlled the ball with one touch and dispatched it with the next.
Benitez began scribbling down his half-time team-talk notes but promptly tore them up.
He had good cause to be annoyed, having looked across the San Paolo pitch to see Fernandez hacking a tame Maurizio Domizzi effort into his own net.
The Argentinian defender did, however, go some way to making amends when play resumed.
When Albiol lost possession in a dangerous area, his fellow centre-back looked alive and denied Nico Lopez a free shot.
After a series of near misses Jose Callejon finally managed to force another save from Zeljko Brkic but it was Udinese who scored next.
Rafael was completely baffled by the 20-metre screamer that beat him in the 70th minute, Fernandes wheeling away to celebrate in front of the travelling fans.
His joy was shortlived, though, as Dzemaili scored the fifth goal, sparking an explosive finish to the match.
Higuain had taken the shot that Brkic did well to parry but Swiss midfielder Dzemaili stepped forward to nudge the ball over the line.
Rafael was still cheering when Maicosuel bore down on him from the restart - the Napoli keeper threw up a hopeful arm and made the save.
The danger had passed, for several minutes, but it came back with a vengeance in the form of Basta.
Once again Napoli's defence was found wanting as Udinese's Serbian winger won the battle of wills that developed from a badly-defended corner.
And amid the madness visiting of a chaotic finale, visiting coach Francesco Guidolin was sent to the stands for demanding punishment for Christian Maggio, who had made a desperate goal-saving tackle on Maicosuel.