Bayern struck first with only two minutes on the clock when Toni Kroos was allowed acres of space inside the Napoli box before placing his shot into the corner.
Napoli, who have not lost at home since returning to European competition three years ago, equalised on 39 minutes when Christian Maggio's right-wing cross was deflected into the net by Holger Badstuber's lunging dive.
Bayern piled on the pressure after Gomez had his 49th-minute penalty saved but Napoli held on, with the result leaving the Germans top of the group on seven points with Napoli in second place on five. Manchester City lie third on four.
Napoli coach Walter Mazzarri said he was delighted to be second at the halfway point of the group.
"Some people said that at this stage we would be bottom," he told reporters. "We haven't set targets so after each game we have to see where we are.
"Our boys are not used to games like these. After their goal we changed tactics and played a great game. This is one of the best sides in Europe - they've won twice already in the group. In the end, we could even have won it."
Bayern coach Jupp Heynckes said the draw was a crucial step towards qualification to the knockout stages.
"I'm not a prophet, but I'm confident now we will qualify," he told reporters. "We came here to win - and I think we deserved the win - but I'm fairly happy with a draw.
"We went at Napoli at the start, controlled the game and stayed tight at the back. Napoli played with a lot of heart and I think they stand a good chance of qualifying too."
The German giants made the perfect start on two minutes when Kroos collected Thomas Muller's pass and ran through the heart of the Napoli defence before calmly side-footing the ball past De Sanctis's despairing dive to silence the home fans.
Napoli tried to respond to the body-blow immediately, but Hugo Campagnaro's seventh-minute drive whistled the wrong side of the post.
Bayern, whose impressive early season form under Heynckes has seen them open up a five-point lead in the Bundesliga, began to boss things. Gomez, shooting wide from the edge of the box, and Jerome Boateng, volleying a corner across the face of goal, almost doubled their lead.
The Napoli attacking trio were failing to fire but they equalised against the run of play six minutes before half-time when Maggio, breaking down the right, saw his cross-shot take a small but damaging deflection off Badstuber, wrong-foot Manuel Neuer and nestle in the net to ignite the San Paolo.
There was more deafening noise after half-time but jeers when Paolo Cannavaro was adjudged to have handled Gomez's fierce shot. The cheers returned when De Sanctis dived to his left to save Gomez's weakly hit spot-kick.
Muller should have given Bayern the lead on 54 minutes but poked his effort wide of goal after another dangerous corner produced an almighty scramble in the Napoli area.
Napoli, back in Europe's premier competition fo
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.