Bremen initially held their own, but strikes from Arjen Robben and Javi Martinez soon ended any hopes Thomas Schaaf's men might have had of picking up points. Bayern hit four in the second half, with Bremen's only consolation coming through Kevin de Byrune's strike to become the first player to beat Manuel Neuer in the league this year.
Despite, or perhaps because of, the small ceremony prior to kick-off to honour Jupp Heynckes reaching 1,000 Bundesliga matches as a player and coach, the veteran tactician showed he still has the capacity to spring a surprise or two by naming a much-changed line-up to face Bremen. Robben, Gomez, Xherdan Shaqiri, Diego Contento and Luiz Gustavo were all offered rare chances to shine, with Wednesday evening's DFB Cup quarter-final against Dortmund also perhaps playing a role in the mass rotation.
Such is the strength of the league leaders' squad, they can offer like-for-like replacements without suffering a dip in quality and the hosts immediately seized the initiative once more. However, against their deep-lying visitors Bayern found scoring chances limited and looked most threatening early on from the vicious set-pieces from either flank by Robben and Franck Ribery.
Eventually cracks began to appear in the Bremen bulwark midway through the first half. Gomez was unable to finish from close range following a superb dummy from Shaqiri, but Robben made no mistake shortly afterwards, volleying home from Philipp Lahm's right-wing cross. Having mainly been used as a substitute recently, the Dutch international was relentless all match and served a sumptuous free-kick minutes later, leaving Martinez the simplest of headers from six yards.
Bremen's afternoon went from bad to worse on the stroke of half-time, when Martinez's exquisite defence-splitting pass played Gomez through, only for the striker to be up-ended by Sebastian Prödl, who was given a straight red card for his troubles. Bayern inevitably went for the jugular immediately after the restart and two quickfire goals ended the game as a contest.
The Bavarians tore at their guests, who offered little resistance as first Gomez outmuscled Lukas Schmitz on the left, before his cross was turned in by Bremen defender Gebre Selassie. Gomez himself put the result beyond all doubt when poking home from close range for his100th career strike for the club following Ribery's lofted pass.
A stunned silence engulfed the Allianz Arena when Manuel Neuer was beaten for the first time in 576 Bundesliga minutes - and the first time in the league in 2013 - when De Bruyne tucked Aleksandar Ignjovski's miscued shot home, but Bayern's victory was never in any danger. Ribery capped off a fine individual display with a well-taken volley on the turn, before Gomez rifled home his own second late on, but by then the damage had already been done in what was truly a Bayern masterclass.
Jonathan Stockitt reporting from Munich
Line-ups and statistics