Steve Bruce’s side were rarely troubled once Scott Hogan’s 18th-minute header gave them the lead.
Kieran Dowell forced a fine save from Sam Johnstone late on, but the Villa keeper was otherwise relatively untroubled as the visitors defended stoutly – and Forest looked short of ideas.
It meant a disappointing start for former Middlesbrough boss Karanka, who agreed to become the permanent replacement for Mark Warburton on Monday, while Villa moved up to fourth in the Championship.
The first half was a story of Forest dominating possession but Villa creating the better chances.
With John Terry marshalling things in the centre of defence, Forest were finding it hard to carve out opportunities.
Ben Brereton failed to properly connect with a headed chance when picked out by a whipped in cross from Eric Lichaj.
And Matty Cash failed to muster enough power in his low shot to trouble Johnstone, who made a simple save.
A superb cross from Robert Snodgrass, along with some questionable Forest defending, was to prove to be the first-half turning point, as keeper Jordan Smith and the rest of his defence hesitated while Hogan ghosted in unmarked to head Villa into the lead.
Snodgrass was the architect again when he picked out Terry, with the former England captain rattling the crossbar with a thumping header.
Ben Osborn and Cash both had shots well blocked on the edge of the box as Forest attempted to muster a response. But the closest they came to an equaliser before the break was a curling…