The former Toulouse striker scored in both legs of Sevilla's qualifying play-off against Istanbul Basaksehir, as well as netting against Liverpool in their opening group game, and was in sparkling form in Tuesday's encounter.
Having already forced Maribor's Jasmin Handanovic into a succession of fine saves, Ben Yedder made no mistake from point-blank range after being teed up by the excellent Joaquin Correa 27 minutes in.
It took Ben Yedder just 11 minutes to double his tally, drilling a low effort in off the post to put Sevilla – whose coach was in the stands following his sending off at Anfield – in cruise control.
But Ben Yedder had to wait until late in the second half – during which Jesus Navas hit the woodwork – to net his third, drilling in from the penalty spot to join Luis Fabiano as Sevilla's second highest Champions League goalscorer on six goals, one shy of Frederic Kanoute, the Andalusians' record scorer in the competition.
And with Spartak Moscow and Liverpool sharing the points in the group's other encounter, Sevilla, who travel to Russia in their next Champions League outing, now lead the way with four points from their opening two fixtures.
Sevilla looked sharp from the off, Ben Yedder – who netted inside five minutes on Merseyside on matchday one – bringing an early save out of Handanovic.
Ben Yedder was almost put through by Marwan Kabha's sloppy back pass shortly after, though Maribor did pose a threat on the counter-attack, with the energetic Marcos Tavares flashing a low warning shot across the face of Sergio Rico's goal.
Rico's counterpart was soon forced into action again at the other end, doing well to keep out Ben Yedder's powerful near-post header.
Ben Yedder was not to be thwarted the next time, however, as – at the culmination of a fantastic run from Correa – the Frenchman tucked home his fifth goal of the season.
Sevilla had appeals for a penalty dismissed as they piled on the pressure, but it was not long until the hosts doubled their lead.
Having latched onto Franco Vazquez's slide-rule pass, Ben Yedder kept his composure to slot precisely across Handanovic.
Berizzo's side maintained the pressure after the restart, although Rico had to be alert to keep out Mitja Viler's attempt.
Ben Yedder could have made it three on the hour when he found himself unmarked in the six-yard box, but Handanovic was out swiftly to smother the danger.
Sebastien Corchia was the next to try his luck as Sevilla looked to put the result beyond all doubt – Handanovic equal to the full-back's rasping drive.
Sevilla did not let up and, after substitute Navas clipped the crossbar with a looping effort, Ben Yedder finally got the chance to seal his hat-trick when Corchia was brought down by Aleks Pihler.
Ben Yedder stepped up confidently, thumping a low strike into the right-hand corner to mark a memorable night and add gloss to a comfortable victory.