The Dragons led 19-5 at the interval on home soil thanks to an Aled Brew score and 14 of Tovey's haul while Giovanbattista Venditti crossed for Aironi.
The game was put beyond doubt after the break as Adam Hughes crossed twice while replacement Aironi prop Fabio Staibano was sent off for a second sin-bin offence.
Elsewhere, tries from Isa Nacewa and Dominic Ryan were enough for Leinster to continue their Magners League revival with a 18-6 Irish derby triumph at Connacht.
Fijian wing Nacewa scored the only try in a closely-fought first-half as the visitors lead 5-3 at the interval.
Ireland prospect Ryan clinched victory with a stoppage time score after intercepting Frank Murray's pass to deny the hosts a losing bonus point.
Jonny Sexton converted to complete an eight-point haul and secure Leinster's fourth straight win in all competitions and their first win in Galway since 2008.
Sunday's action see Glasgow Warriors, still seeking their first win since the opening weekend of the season, taking on defending Magners League champions Ospreys.