Borussia Dortmund's lead was cut to 10 points after they conceded a 90th-minute equaliser to draw 1-1 at Kaiserslautern.
The stunning performance by Robben and Ribery arrived at a good time, with Bayern's Champions League last-16 clash with holders Inter Milan coming up later this month.
"We can play even better than that," Robben told reporters. "Our game was good but it was not just Franck and me. Today we wanted to set the record straight and show we are a super team."
Both players have had to battle against injury, with Robben missing the first half of the season, but they were in scintillating form on Saturday as the Dutchman scored twice and set up another goal and the Frenchman created two.
The win lifted Bayern to third spot on 39 points, three behind Bayer Leverkusen who won 3-0 at Eintracht Frankfurt even though Michael Ballack was surprisingly left on the bench. Dortmund have 52 points.
"We have so much more creativity up front with Robben and Ribery," said Bayern coach Louis van Gaal who has been under pressure since the 3-2 defeat by Cologne last week.
GOMEZ GOAL
It took Robben only 90 seconds to make an impact when he set up Bundesliga top scorer Mario Gomez for his 17th goal of the season.
The Dutch forward then struck for the hosts with a spectacular solo effort in the second half after Frenchman Ribery had set up Thomas Muller for the second goal in the 15th minute.
The 'Robbery' show, to use the affectionate nickname for the duo, was complete in the 81st minute when Ribery crossed from the left and Robben controlled the ball before curling a trademark left-footed shot into the top corner.
Dortmund thought they had won a tough game when Sven Bender slotted home from close range eight minutes from time at Kaiserslautern.
Three minutes later though Dortmund central defender Neven Subotic was sent off for a second caution. The hosts made the most of the extra player, pouring forward for Jan Moravek to grab the equaliser with a powerful shot from the edge of the box.
Champions League competitors Schalke 04 beat Freiburg 1-0 to ease the pressure on coach Felix Magath as his team moved up to 10th on 29 points.
Second from bottom VfB Stuttgart slumped 4-1 at home to Nuremberg while Borussia Moenchengladbach stayed bottom after losing 3-1 at St Pauli.
