Schalke 04, who started the weekend in second place, finished in fifth after drawing 2-2 at Hannover 96 despite two goals from Teemu Pukki on his first Bundesliga start.
The irrepressible Gomez scored his 13th Bundesliga goal of the season and his 20th in all competitions to set Bayern on the way against promoted Augsburg, who have yet to win a home game.
Gomez was on hand to nod in in the 16th minute after Daniel van Buyten headed on a corner at the far post and goalkeeper Mohamed Amsif could only push the ball into the path of the Bundesliga's top-scorer.
Franck Ribery weaved his way past two defenders to add the second in the 28th minute with Bayern apparently on automatic pilot despite the absence of injured captain Bastian Schweinsteiger.
But Augsburg, bottom with eight points and only one win, made life uncomfortable when Japanese forward Hajime Hosogai pulled one back in the 59th minute, scoring from close range after Bayern failed to clear a corner.
Edmond Kapllani had a golden chance to equalise in the 82nd minute when he broke clear but the Albanian's shot was brilliantly saved by Neuer.
Bayern had Anatoliy Tymoshchuk sent off in the last minute for a clumsy challenge on Daniel Baier whose triple somersault appeared to be a complete over-reaction.
The Bavarians, who have won nine of their 12 games, lead with 28 points, five clear of Borussia Dortmund, Werder Bremen and Borussia Monchengladbach, who all won on Saturday.
Schalke are a further point behind in fifth.
They went ahead in the 26th minute at Hannover with an individual goal from Pukki, who burst past two defenders and rounded goalkeeper Ron-Robert Zieler to score into an empty net.
The lead lasted only three minutes before Greek defender Kyriakos Papadopoulos headed into his own goal as he tried to clear Jan Schaudraff's free-kick.
Mohammed Abdellouae put Hannover ahead with his eighth goal of the season just before the hour and Pukki levelled from Jefferson Farfan's pass in the 73rd minute.
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