The Czech striker almost netted a second goal before the quarter-hour mark, but his close-range effort cannoned off the crossbar and went clear.
Wolves were having plenty of the ball in the final third, but their best effort in the opening 25 minutes came from James Henry, who dragged an 18-yard effort wide.
A low effort from Gabriel Agbonlahor that was smothered by Ikeme ensured that Villa began the second half on the front foot, but Wolves almost found an equaliser when Nouha Dicko fired straight at Mark Bunn after meeting a cross at the back post.
On 72 minutes though, Wolves did get back on level terms through David Edwards, who flicked a cross from Iorfa into the net from close range.
However, five minutes later, Villa retook the lead through Kozak after he slid in at the back post to divert a miscued shot from Callum Robinson.
It appeared as though that would be enough to earn Tim Sherwood's side the win, but with a minute remaining, Afobe collected a pass from Conor Coady before coolly finishing past the goalkeeper. body check tags ::