The seven-time champion kept his hopes of an eighth title alive courtesy of a 6-3 7-5 6-3 victory on Centre Court to move into the last-32 stage at SW19.
Despite being ranked 103 in the world, Muller kept the fifth seed at arm's length early on in the opening set, but a break of serve allowed the Swiss to break away and seal an early advantage in comfortable fashion.
Muller continued to prove a pest in the second set as little could separate the pair after seven games, with Federer leading 4-3.
The contest was then stopped as the rain began to pour on Centre Court, but the break of play to facilitate the closure of the roof did not knock Federer out of his stride as he swiftly took a two-set lead once the match resumed.
Muller's resistance gradually waned in the final set, however, as another break of serve helped Federer - who was not broken in the match - take a 3-1 lead en route to the victory.