The match-winning moment arrived 18 minutes into the contest after a dangerous cross from Robert Snodgrass was pounced on by Hogan, giving the Villans a first league win at this ground since January 1995.
Villa, who also pulled off a league double over the Reds for the first time since 1992-93, find themselves fifth in the Championship table and five points adrift of the automatic promotion zone.
The visitors took the lead with 18 minutes on the clock, however, thanks to a first-time finish from Hogan, who profited from a tasty Snodgrass cross that Forest could not deal with.
Not since last February have Villa lost a game once taking the lead, and they looked good value to keep that run going when skipper John Terry came within inches of bagging a second, hitting the woodwork with his headed attempt from six yards.
Kieran Dowell offered the hosts' best response before the break, curling a shot wide of the target as Karanka's men were left staring at defeat with half the game to play.
Star man Snodgrass continued to terrorise the Forest defence with his deliveries as the match transpired, and he almost caught out Jordan Smith at his near post with 52 minutes on the clock.
A near-miss from Jack Grealish gave the Reds further food for thought, but they did eventually grab a foothold on the match as Barrie McKay tested Johnstone and Cash had a good headed chance which he could not make the most of.
Johnstone thwarted McKay for a second time in the final 10 minutes of the game, while up the other end the Villans also pressed for a goal but could not find the net.
Grealish wasted a good opening from 20 yards and Albert Adomah had a late strike ruled out for offside, leaving the game delicately poised in the dying stages.
Neither Dowell nor Jamie Ward could find a way through with their attempts, however, as Villa claimed the points to end their City Ground hoodoo.
NOTTINGHAM FOREST (4-2-3-1): Smith; Lichaj, Mills, Mancienne, Traore; Vaughan (Ward 81'), Osborn; Cash (Bridcutt 81'), Dowell, Clough (McKay 64'); Brereton
ASTON VILLA (4-5-1): Johnstone; Elmohamady, Chester, Terry, Hutton; Snodgrass, Whelan (Bjarnason 46'), Hourihane, Adomah (Taylor 91'), Grealish; Hogan (Davis 83')