Massimiliano Allegri's men have failed to light up Serie A so far this season with five points from their opening four games and looked set for another difficult night against their Czech opponents.
But Ibrahimovic grabbed his chance to ease the tension and when Antonio Cassano converted his side's second goal in the 66th minute Allegri was finally able to breathe a sigh of relief.
It was only Milan's second win in four matches since a creditable 2-2 draw in their opening Group H fixture against Barcelona at the Nou Camp earlier this month.
It might have been much easier for the home side had Ignazio Abate's dangerous cross with just 28 seconds on the clock not been brilliantly saved by Plzen goalkeeper Marek Cech with danger lurking.
But the visitors quickly went on to serve notice of their intentions as Milan Petrzela met a Vaclav Pilar cross with a firm header in the centre of the penalty area which produced a fine save from Christian Abbiati.
Plzen came into the game with confidence after a solid start to their new Czech Liga season, a run of five games unbeaten keeping them well in touch with the league leaders.
In a lively start Cech saved twice from the dangerous Cassano then Mark Van Bommel came close to breaking the deadlock in the 13th minute when he headed an Abate cross over the bar.
Cech saved again from Cassano but Plzen continued to look lively and both Marek Bakos and Petr Jiracek fired wide from long range.
Pavel Horvath had the first chance of the second half for Plzen but Milan got their chance shortly afterwards when Marian Cisnovski's handball in the box allowed Ibrahimovic to step up and slam home the penalty.
Cassano shot over the bar but Milan's lead looked anything but safe with Abbiati forced into action again to deny Horvath, then Clarence Seedorf booting clear a free-kick from the same player.
The points were finally all but guaranteed for the home side in the 66th minute when Cassano met Ibrahimovic's cross from the left with a right-foot shot into the bottom corner.
The game lost much of its momentum after the home side's second goal but the visitors continued to do their best to press forward and a shot by Michal Duris was blocked in the box by Van Bommel.
Two minutes later Daniel Kolar tried his luck from 30 yards but his speculative effort was easily saved by Abbiati as Milan cruised to a victory which they must hope will settle their nerves ahead of their next Group H tie against BATE Borisov.