Rodriguez Hits Hat-Trick As Bayern Return Top
Bayern coach Niko Kovac had urged his team to respond following Wednesday's Champions League exit at the hands of Liverpool, and Mainz bore the brunt of the backlash at Munich's Allianz Arena.
Rodriguez, on loan until the end of the season from Real Madrid, came off to a standing ovation with 20 minutes to go after arguably his best display in the famous red shirt.
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Canadian wunderkind Alphonso Davies, 18, also scored his first Bayern on only his fifth appearance after coming off the bench.
The thumping win saw Bayern reclaim top spot in the Bundesliga from Borussia Dortmund, who briefly usurped them with a nervy 3-2 win at Hertha Berlin on Saturday.
Poland striker Robert Lewandowski, the Bundesliga's top scorer, claimed his 18th league goal this season by tapping in a David Alaba cross on three minutes with many Bayern fans still searching for their seats.
Leon Goretzka laid on the second goal, chesting down into Rodriguez's path and the Colombian opened his account on 33 minutes.
French winger Kingsley Coman showed clinical finishing six minutes from halftime as his shot gave Mainz goalkeeper Florian Mueller no chance to make it 3-0 at the break.
Rodriguez wrapped up his hat-trick with two goals in four breathtaking minutes, hitting the top corner past Mueller's reach on 51 minutes, then chipping the despairing Mainz goalkeeper moments later.
Just 11 minutes after coming on, Davies was rewarded with his first Bundesliga goal, netting the rebound from a saved Lewandowski shot.
Bayern have now scored 17 goals in three league games and have won 13 of their last 14 matches in the Bundesliga.
FRANKFURT MARCH ON
Earlier, fifth-placed Eintracht Frankfurt, the only Bundesliga club left in European football, maintained their challenge for a Champions League spot with a 1-0 win at home to bottom side Nuremberg.
A first-half goal by Austrian defender Martin Hinteregger left Frankfurt unbeaten in their last 13 games, including nine in the Bundesliga.
Frankfurt face Benfica over two legs in the Europa League quarterfinals after beating Inter Milan 1-0 last Thursday, and a superb pass from in-form striker Luka Jovic, on loan from the Portuguese side, led to Sunday's winner.
The 21-year-old Serbian, who scored in Milan, has netted 15 goals in 24 league games this season, including five against Fortuna Duesseldorf last October.
He set up the winner by spotting Filip Kostic free on the left and Jovic's pin-point accurate pass found his Serbian teammate, who crossed for Hinteregger to tap home on 31 minutes.
Earlier, Werder Bremen forwards Max Kruse and Milot Rashica combined in a shock 3-1 win at Bayer Leverkusen.
Between them, centre-forward Kruse and winger Rashica have netted six goals and provided three assists in four league games and the duo did the damage against Leverkusen.
Kruse gave his mid-table side the lead on 13 minutes and helped double the lead at the BayArena when he set up Rashica, who grabbed his third goal in two games after a brace in last week's 4-2 rout of Schalke.
Leverkusen's Jamaican winger Leon Bailey blasted home a free-kick on 75 minutes, but with the hosts chasing an equaliser, Bremen counter-attacked and Kruse cut in to drill home his second in the 95th minute.
The result lifts Bremen to eighth and leaves Leverkusen sixth, four points behind Frankfurt.