Paddy Wallace, who was in outstanding form all night, grabbed the first try before a penalty try and a Rory Best effort gave Ulster a 24-7 lead, Tito Tebaldi getting a try back for Aironi.
After the break Ulster continued to dominate and after Cave's effort, Tom Court and Pedrie Wannenburg got in on the act.
It was Aironi who could have taken the lead after just nine minutes as Sinoti Sinoti produced a scintillating break stepping inside several tackles before being stopped ten metres short of the line.
However the home side fought back well and on their next incursion into Italian territory Chris Henry was held just short but after some quick recycling Ian Humphreys threw a pop pass to Wallace who breezed straight through for a try, converted by Ruan Pienaar.
Ulster's dominance up front was proving decisive and they were rewarded with a penalty try after three scrums on the Aironi five-metre line to make it 14-0 with 23 minutes gone.
Just after the half hour Brian McLaughlin was handed a big blow when Stephen Ferris was forced off with an injury and Aironi took full advantage scoring from a cleverly-worked lineout immediately after.
The Italians threw to the front opening up a gap in the lineout which allowed Tito Tebaldi to dart through a gap and dive over, Naas Olivier added a tough conversion.
Having let Aironi back into it, Ulster immediately went on the offensive and Pienaar slotted the penalty after the Italians were penalised for going off their feet.
It got worse for Aironi soon after when Giulio Toniolatti was sent to the sin bin for hands in the ruck and from the ensuing lineout Best went over from a driving lineout to stretch the lead to 24-7 at half-time.
The second half began in the same way as the first ended with Cave combining well with his centre partner Wallace to cross for the bonus point score.
And after being frustrated as a raft of replacements caused the game to lose its rhythm, Court finished off a move started by replacement Adam D'Arcy, producing a great sidestep to barge over from close range.
With eight minutes remaining Wannenberg picked up from the back of a scrum before throwing a dummy and going through the ensuing gap for the sixth try.
|Ulster Rugby Score Card|
|Aironi Rugby Score Card|