Howson volleyed in the opener from Nathan Redmond's cross midway through the first half and that was how it stayed until three minutes from time when Mbokani headed home the second.
It was a second win in three for Alex Neil's side to edge them away from the relegation zone while Villa remained rooted to the foot of the table with their hopes of survival slimming by the week.
Villa were certainly the better side in the opening stages with Scott Sinclair looking particularly bright down the right.
He was involved a the move that eventually saw the ball come to Leandro Bacuna 25 yards out and he tested Declan Rudd with the first shot of the match.
From the resulting corner, Micah Richards was inches away from giving Remi Garde's side the lead. The ball dropped on the six-yard line and under pressure from his marker, Richards was unable to stab the ball goalwards.
The visitors continued to press and fashioned the best chance of the half, Ashley Westwood's free-kick finding Jordan Ayew whose header forced Rudd to parry the ball away, diving to his left.
Villa were well on top but it counted for little as they fell behind soon after. Redmond played a neat one-two with Graham Dorrans to get into the Villa box and clipped in a cross that skimmed off a defender's head and into the path of Howson, the midfielder making no mistake with his volley from eight yards.
Jonny Howson celebrates after putting Norwich in front
Despite a decent response from Villa, Norwich could have doubled their lead as a smart corner routine saw Dorrans fire just wide of the near post from a low delivery.
It was a similar story in the second half as Villa again started on the front foot but were unable to create any real openings.
In truth, neither side looked particularly threatening and when Norwich did have the chance to add a second, it came out of very little.
Redmond tried his luck with a shot form 25 yards that bounced just in front of Guzan and when the 'keeper spilled it, the ball ran to Howson on the edge of the box.
However, on this occasion the midfielder was unable to find his mark and slid the ball narrowly wide.
Ayew briefly caused panic in the Norwich defence with a powerful run through the middle before oddly choosing to pass out wide having reached the edge of the area with just one defender ahead of him.
Soon after, a Ciaran Clark slip nearly allowed Mbokani to run through on goal but the defender recovered to make a crucial slide tackle to deny the striker.
At that point the game seemed destined to end 1-0 but another defensive lapse, this time from Alan Hutton, allowed Norwich the chance to clinch the win and this time they were clinical.
Redmond found Hoolahan on the edge of the box and he delivered a perfect cross to Mbokani, who had peeled away to the far post.
The rest seemed merely a formality, the striker planting the header past Guzan to wrap up all three points.
There was still time for Ayew to draw a fantastic save out of Rudd with a curling free-kick in the final minute of stoppage time before the final whistle went and Norwich were able to celebrate a crucial win.
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