The Germany Under-21 forward opened the scoring when his third-minute shot looped in off keeper Jonas Lossl.
Emil Forsberg slotted in a second, then cut a ball back for Werner to make it 3-0 at half-time.
Scottish teenager Oliver Burke replaced Werner moments before Stefan Bell headed a consolation goal for Mainz.
Bayern lead the table only on goal difference, having drawn 1-1 at home to Hoffenheim on Saturday.
Match ends, RB Leipzig 3, 1. FSV Mainz 05 1.
Second Half ends, RB Leipzig 3, 1. FSV Mainz 05 1.
Corner,  1. FSV Mainz 05. Conceded by Stefan Ilsanker.
Attempt missed. André Ramalho (1. FSV Mainz 05) header from very close range is too high. Assisted by Yunus Malli with a cross following a corner.
Corner,  1. FSV Mainz 05. Conceded by Willi Orban.
Foul by Davie Selke (RB Leipzig).
Stefan Bell (1. FSV Mainz 05) wins a free kick in the defensive half.
Naby Keita (RB Leipzig) wins a free kick in the defensive half.
Foul by Stefan Bell (1. FSV Mainz 05).
Foul by Marcel Halstenberg (RB Leipzig).
Giulio Donati (1. FSV Mainz 05) wins a free kick on the right wing.
Corner,  1. FSV Mainz 05. Conceded by Marcel Halstenberg.
Substitution, RB Leipzig. Dominik Kaiser replaces Emil Forsberg.
André Ramalho (1. FSV Mainz 05) is shown the yellow card for a bad foul.
Davie Selke (RB Leipzig) wins a free kick in the defensive half.
Foul by André Ramalho (1. FSV Mainz 05).
Attempt saved. Gaëtan Bussmann (1. FSV Mainz 05) right footed shot from the centre of the box is saved in the centre of the goal.
Offside, 1. FSV Mainz 05. André Ramalho tries a through ball, but Karim Onisiwo is caught offside.
Hand ball by Marcel Sabitzer (RB Leipzig).
Foul by Oliver Burke (RB Leipzig).
Alexander Hack (1. FSV Mainz 05) wins a free kick in the defensive half.
Stefan Bell (1. FSV Mainz 05) is shown the yellow card for a bad foul.
Emil Forsberg (RB Leipzig) wins a free kick in the defensive half.
Foul by Stefan Bell (1. FSV Mainz 05).
Substitution, RB Leipzig. Davie Selke replaces Yussuf Poulsen.
Attempt blocked. Daniel Brosinski (1. FSV Mainz 05) right footed shot from outside the box is blocked.
Foul by Diego Demme (RB Leipzig).
Yunus Malli (1. FSV Mainz 05) wins a free kick on the left wing.
Oliver Burke (RB Leipzig) wins a free kick in the attacking half.
Foul by André Ramalho (1. FSV Mainz 05).
Goal!  RB Leipzig 3, 1. FSV Mainz 05 1. Stefan Bell (1. FSV Mainz 05) header from very close range to the top right corner. Assisted by Alexander Hack with a headed pass following a corner.
Corner,  1. FSV Mainz 05. Conceded by Willi Orban.
Attempt blocked. Gaëtan Bussmann (1. FSV Mainz 05) right footed shot from the left side of the box is blocked.
Attempt missed. Emil Forsberg (RB Leipzig) left footed shot from the centre of the box is high and wide to the left. Assisted by Yussuf Poulsen following a fast break.
Attempt blocked. Yussuf Poulsen (RB Leipzig) right footed shot from the centre of the box is blocked. Assisted by Naby Keita.
Marcel Sabitzer (RB Leipzig) wins a free kick in the defensive half.
Foul by Gaëtan Bussmann (1. FSV Mainz 05).
Substitution, RB Leipzig. Oliver Burke replaces Timo Werner.
Foul by Yussuf Poulsen (RB Leipzig).
André Ramalho (1. FSV Mainz 05) wins a free kick in the attacking half.
RB Leipzig moved level on points with Bundesliga leaders Bayern Munich after Timo Werner scored twice in a comfortable 3-1 win over Mainz.