Nigerian Yakubu gave Portsmouth's survival hopes a boost with his sixth goal of the season early in the second half but Vassell struck home Villa's winner seven minutes from time.
When Yakubu cancelled out Angel's 22nd minute strike five minutes into the second half it was Portsmouth's first away goal since they scored against Arsenal on September 14.
Surprisingly Portsmouth left their leading marksman, Teddy Sheringham, on the bench. Manager Harry Redknapp felt the former England striker deserved a break following a spell in which he has been an ever-present.
Villa were themselves unable to raise their game to the heights they achieved against Manchester United on Sunday.
But they were generally well in control against a struggling Pompey side that is rapidly sinking deeper into trouble.
Villa deservedly took the lead in the 22nd minute when Gareth Barry collected a quick throw-in from J Lloyd Samuel and hammered a long left-wing cross to the far post where the agile Angel was on hand to head past Pavel Srnicek to record his 14th goal of the season.
Only the woodwork saved Pompey slipping further behind when Lee Hendrie shot on the turn, only to see his effort hit the angle of the post and bar.
On-loan Jason Roberts, who is wanted by Wigan Athletic, was industrious but lacked a service to be of any real danger to Villa's stand-in central defender, Dion Dublin.
Matthew Taylor, who was involved in several anxious moments attempting to contain Vassell, produced Portsmouth's best goal attempt with a curling inswinger that Thomas Sorensen flicked over the bar.
Sorensen was in trouble with a low shot from Alexei Smertin that he fumbled away for a corner as Portsmouth made a spirited bid to get on level terms.
They achieved their objective five minutes into the second half when slack marking by Villa's defence enabled Yakubu to head home Patrik Berger's free-kick.
Vassell's 83rd minute winner came after a Barry free-kick found Olof Mellberg. His shot was blocked into the path of the England striker who tapped the ball home from close range.