Lewandowski treble sees Bayern through in German Cup
The Poland striker put Bayern ahead after just three minutes at fourth-division club Jena, the former East German champions who have fallen from grace, combining with Thomas Mueller before slotting home.
Lewandowski then tapped in from close range after Franck Ribery's pass found him in the area on 34 minutes.
He rolled another shot past Jena goalkeeper Raphael Koczor nine minutes later to claim his third and leave Bayern 3-0 up at the break.
Chile midfielder Arturo Vidal netted the fourth, converting Lewandowski's final pass on 72 minutes having twice hit the woodwork.
Centre-back Mats Hummels then netted his first goal for Bayern with a late header.
The cup tie had the air of a competitive training session for Bayern, who fielded a full-strength starting side who had all played international football in the close season.
Bayern open the new Bundesliga season next Friday when the defending champions host Werder Bremen.
The Bavarian giants are chasing a fifth consecutive German title, with Carlo Ancelotti having succeeded Pep Guardiola as head coach.
The win at Jena was a sweet return for Ancelotti, 36 years after he played in a Roma side which was on the wrong end of a 4-0 hammering at the Ernst Abbe Sportfeld stadium in the Cup Winners' Cup.
Elsewhere, Bundesliga outfit Augsburg won 2-0 at fifth-division team Ravensburg, who had forward Rahman Soyudogru sent off late on.
South Korea midfielder Koo Ja-Cheol gave the visitors an early lead before Raul Bobadilla added a second.
Second-division Hamburg-based St Pauli are also into the second round after a 3-0 win at fourth-tier Luebeck.
The first-round action continues across the weekend, with last season's runners-up Borussia Dortmund going to minnows Eintracht Trier on Monday.