Left-winger Kingsley Coman also failed to capitalise on an opportunity,  lacking the accuracy to convert a one-on-one with Paderborn goalkeeper Jannik Huth.

After 15 minutes and several near misses, right winger Serge Gnabry eventually connected with a Coutinho cross to give Bayern the advantage.

That advantage nearly disappeared, however, when Thiago Alcantara came close to handing the hosts an equaliser with an own goal.

The scoreline remained unchanged as half-time approached, with Coutinho and Gnabry falling short when presented with chances for a second Bayern goal.

Paderborn then reemerged from the break with conviction, looking threatening in the opening moments of the second half.

But it was Gnabry who took the initiative again, passing to an unmarked Coutinho who neatly put away his first Bundesliga goal from open play to give the Bavarians a two-goal lead.

Gnabry threatened a second goal in the 65th minute but saw his shot comfortably dealt with by Huth.

The hosts refused to fold and midway through the second half Tunisian midfielder Mohamed Drager found Kai Proger on the right wing and the latter fired a low shot past Neuer to make it 2-1.

The goal seemed to reinvigorate Paderborn, who battled to take control from Niko Kovac's side as the game neared its conclusion.

Their resurgence was halted in the 80th minute when Lewandowski picked up a Niklas Sule pass and made it 3-1 to Bayern with his 10th goal in six Bundesliga matches.

However, Jamilu Collins halved the deficit with six minutes remaining, firing home a superb long-range shot.

Muller then linked up with Coutinho to find Gnabry as Bayern pushed to distance themselves from Baumgart's squad – but the resulting effort was wide.

An injury-time free-kick provided Bayern with a final opportunity, but Coutinho's shot was off target.