Bayern's emphatic victory boosted their confidence ahead of the Champions League round of 16 second leg against Basel in midweek and gave them 51 points from 25 games.
Dortmund's draw ended an eight-match winning streak but also equalled a club record of 19 consecutive games without defeat.
Gomez gave Bayern a fifth-minute lead when he pounced on a weak clearance by goalkeeper Tom Starke, opening the floodgates as the hosts looked to bounce back from last week's defeat by Bayer Leverkusen.
Bayern scored four more times in the first half through Gomez, a goal and a penalty from Dutchman Robben and Toni Kroos as Hoffenheim kept losing possession deep in their own territory.
Bundesliga top scorer Gomez notched his third goal of the game with a header at the far post in the 48th minute to take his league tally to 21 goals this season.
Franck Ribery made it 7-0 following a quick break before former Hoffenheim player Luiz Gustavo put through his own net with five minutes to go.
"We played ourselves into a trance and the goals were absolutely delicious," Bayern coach Jupp Heynckes told reporters.
"The difference with our game against Leverkusen was that we played well for 90 minutes and made the most of our chances."
There was more good news as midfielder Bastian Schweinsteiger made his comeback from injury with a second-half appearance as Bayern continue to chase a Bundesliga-German Cup-Champions League treble.
UNBEATEN RUN
Dortmund were shut out by a battling fourth from bottom Augsburg side fighting to avoid relegation.
Kevin Grosskreutz missed the best chance for the champions when his 60th-minute header was palmed wide by keeper Simon Jentzsch and Augsburg's players celebrated wildly at the final whistle.
Third-placed Borussia Monchengladbach lost ground in the title race, drawing 0-0 at home to second from bottom Freiburg to drop three points behind Bayern.
Leverkusen, crushed 7-1 by Barcelona in the Champions League in midweek, lost 3-2 at VfL Wolfsburg and remain in fifth place on 40 points.
Cologne had two players sent off, including Lukas Podolski, in the second half but held on for a 1-0 win over Hertha Berlin who finished with 10 men after a bad-tempered game.
Mato Jajalo of Cologne received his marching orders in the 67th minute while Podolski, who denied media reports he had agreed to join Arsenal at the end of the season, was sent off for grabbing an opponent by the throat in the 76th.
Mohamed Zidan scored for the sixth consecutive game since joining Mainz in the January transfer window to help them to a 2-1 win over Nuremberg.
