Colback opened the scoring at the City Ground inside the first five minutes, delivering a cross from the left flank which caught out Villa ‘keeper Jed Steer and looped into the far corner.
However, that was to be as good as it got for Forest, with John McGinn quickly cancelling out Colback’s strike before the Scot completed a swift turnaround after only a quarter of an hour.
Kortney Hause wrapped things up for Villa in the second half, leaving Martin O’Neill’s side three points shy of a top-six spot with nine games left to play.
Elsewhere, Dwight Gayle and Jacob Murphy were both involved for managerless West Bromwich Albion, who took on Swansea City at the Hawthorns.
Gayle played 90 minutes and Murphy just shy of 70 as the Baggies picked up a 3-0 victory, consolidating their place in fourth in their first outing since the sacking of Darren Moore.