Villa had lost two and drawn one of their first three matches under Lambert, but that frustrating run was ended in convincing fashion at Villa Park thanks to two of the Scot's recent signings.
Right-back Lowton, signed from Sheffield United, broke the deadlock with his first goal for the club in the first-half before Belgian striker Benteke, a ?7 million arrival from Genk, came off the bench to net his maiden Villa goal in the closing minutes.
While Villa are off the mark under Lambert, Swansea's three-match unbeaten run under their new boss Michael Laudrup came to an end despite an enterprising start from the visitors.
It needed two superb reflex saves in the space of 60 seconds from American goalkeeper Brad Guzan to prevent Swansea from taking the lead.
Guzan turned over a powerful close-range header by Ashley Williams, then tipped a 20-yard drive from Nathan Dyer over the bar.
But Villa quickly found their stride and a superb strike from Lowton put them ahead after 16 minutes.
Barry Bannan's corner was headed out by Williams but Lowton brought the ball under control and volleyed an unstoppable shot past Michel Vorm from just inside the area.
Villa kept pushing forward in search of a second goal and Vorm reacted sharply to turn aside Andreas Weimann's snap-shot.
Danny Graham wasted a chance to equalise on the stroke of half-time when the Swansea striker failed to make contact with a low cross from Dyer with the goal at his mercy.
It was Villa who were back on top after the break however and Leon Britton headed a Weimann shot off the line.
Benteke, who had come on for Weimann, saw his strike deflected wide before Ciaran Clark's header was tipped over by Vorm.
But Benteke sealed the win in the 88th minute when he lobbed Vorm after Williams' backpass fell short of tne keeper.
Source: AFP
Source: AFP