But the Welsh region made certain of the win when Tom Riley and Aled Brew crossed for tries, with man-of-the-match Tovey adding one conversion.
The result represented the Dragons' fourth successive victory in all competitions, and completed a season's double over Aironi. The Italians lost 36-5 at Rodney Parade in October.
Experienced full-back Julien Laharrague and flanker Gareth Krause returned to Aironi's starting line-up, with young hooker Tommaso d'Apice earning his first call-up to the bench.
The Dragons were captained by Wales lock Luke Charteris, with regular skipper Tom Willis, who was suspended for this match, set to miss the rest of the season with a thumb injury.
Lloyd Burns took over from Willis at hooker, while Martin Thomas returned at full-back and Pat Leach and Tom Riley replaced the injured Ashley Smith and Matthew Watkins at centre.
Having viewed Aironi's gutsy defeat to Leinster, acting Dragons coach Darren Edwards had the visitors primed for quite a battle and so it proved.
Both sides took their time to settle and when Aironi were presented with the first scoring chance in the 18th minute, scrum half Tito Tebaldi failed to convert his penalty.
Tovey opened the Dragons' account in the 27 minutes and after Aironi were pinged for going offside three minutes later, he doubled his side's advantage.
The young fly-half went on to have quite an influence on proceedings, providing the assists for both of the Dragons' tries.
Tebaldi missed a second penalty before the break, but redeemed himself with a successful kick two minutes into the second half.
Coming up to the hour mark, the Dragons struck for their first try. Winger Will Harries provided the attacking spark and Riley was able to score in the corner following a well-judged cross-field kick from Tovey.
The conversion was added for a 13-3 advantage, but Aironi dug their heels in and their forwards were holding their own in the set piece and in the loose.
Dragons lost flanker Andrew Coombs to the sin-bin. However, Aironi's James Marshall missed the resulting penalty and winger Brew was soon over for the clinching try.
Tovey put boot to ball again, chipping ahead to create the opening for Brew to gather and touch down in the corner, with the conversion attempt bouncing back off an upright.
Aironi had no answer and Rowland Phillips' side were left to rue those missed penalties and defensive lapses out wide, as certainly a losing bonus point looked there for the taking.
|Aironi Rugby Score Card|
|Newport Gwent Dragons Score Card|