With the game already well in hand, Davies entered in the 59th minute against Mainz Sunday and then scored his club's final goal 11 minutes later, pouncing on the rebound opportunity in Bayern's 6-0 rout.
Bayern are level on points with Borussia Dortmund but have the better goal difference by seven.
The 18-year-old Canadian, who moved to Bayern from MLS in January, has yet to start for the German champs. "The last three games are a marker", Mueller added, with Bayern having smashed in 17 goals in winning their last three league games.
Leon Goretzka laid on the second goal, chesting down into Rodriguez's path and the Colombian opened his account on 33 minutes.
Bayern coach Niko Kovac was under pressure to deliver a convincing win after his side were knocked out of the Champions League in the round of 16 by Liverpool last week, and his team responded with their 13th win in their last 14 league games.
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 quarter-finals 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 Hinteregger's victor.
Max Kruse opened and finished the scoring for Werder Bremen to beat Bayer Leverkusen 3-1 away and boost its European qualification hopes on Sunday.
Leon Bailey pulled one back with a brilliant free-kick with 15 minutes remaining but Kruse scored again on the break deep into injury time.
The win lifted Bremen to eighth, three points behind Leverkusen, which occupies the last place for Europa League qualification.