Ulster held off a spirited fight-back from Aironi to complete the Heineken Cup double and cruise to the top of Pool Four with a 46-20 victory.
Aironi came fighting back with tries from Sinoti Sinoti and Roberto Quarteroli before Ulster put the Italians to the sword and wrapped up the bonus point thanks to further scores from Craig Gilroy, Robbie Diack and Adam Macklin.
The victory in Italy sees Brian McLaughlin's men climb to the top of their group two-points ahead of Leicester Tigers in second and three above of ASM Clermont Auvergne in third.
Ulster welcome Leicester to Ravenhill in Round Five before finishing against Clermont Auvergne.
The Irish province got off to a flying start in Monza and Trimble should have scored the game's first try on three minutes. The ball was spread wide and the Ireland wing raced over in the corner but embarrassingly dropped the ball in the process of touching down.
But Trimble quickly saved his blushes with a try beneath the posts two minutes later after bursting on to a Ian Humphreys short ball.
Humphreys added the extras and extended Ulster's lead to 10-0 with a penalty on the 15 minute mark before Luciano Orquera hit back.
English referee Greg Garner awarded Ulster a penalty try on 22 minutes as their pack rumbled towards the whitewash.
Again Humphreys slotted the conversion and a penalty before Court rumbled over for the Ravenhill outfit's third converted try to finish the half leading 27-3.
Ulster made hard work of the second half and Aironi came fighting back with two quick-fire tries.
First Samoan flyer Sinoti scampered over in the corner as Aironi worked the overlap following a sustained period of pressure. Then Quarteroli intercepted Ruan Pienaar's pass at the back of a ruck to sprint clear and bring Aironi back to 27-15.
But Ulster weathered the storm and Gilroy scored the all-important bonus-point try on 69 minutes with Pienaar converting from the touchline.
That did not stop the spirited Italians and Biagi squeezed into the corner to keep alive Aironi's slim hopes at 34-20.
But knowing the importance of tries scored in a tight group Ulster went for the jugular and grabbed late tries through Diack and Macklin.
Tries: Sinoti, Quartaroli, Biagi
Tries: Trimble, Penalty try, Court, Gilroy, Diack, Macklin
Cons: Humphreys 3, Pienaar 2
Pens: Humphreys 2
Aironi: 15 Ruggero Trevisan, 14 Sinoti Sinoti, 13 Andrea Masi, 12 Gabriel Pizarro, 11 Giovanbattista Venditti, 10 Luciano Orquera, 9 Tyson Keats, 8 Josh Sole, 7 Simone Favaro, 6 Nicola Cattina, 5 Marco Bortolami, 4 Quintin Geldenhuys, 3 Lorenzo Romano, 2 Fabio Ongaro, 1 Salvatore Perugini.
Replacements: 16 Tommaso D'Apice, 17 Alberto de Marchi, 18 Fabio Staibano, 19 George Biagi, 20 Filippo Ferrarini, 21 Tito Tebaldi, 22 Naas Olivier, 23 Roberto Quartaroli.
Ulster: 15 Adam D'Arcy, 14 Andrew Trimble, 13 Darren Cave, 12 Nevin Spence, 11 Craig Gilroy, 10 Ian Humphreys, 9 Ruan Pienaar, 8 Pedrie Wannenburg, 7 Chris Henry, 6 Stephen Ferris, 5 Dan Tuohy, 4 Johann Muller (capt), 3 John Afoa, 2 Rory Best, 1 Tom Court.
Replacements: 16 Nigel Brady, 17 Paddy McAllister, 18 Adam Macklin, 19 Tim Barker, 20 Robbie Diack, 21 Paul Marshall, 22 Paddy Jackson, 23 Stefan Terblanche.
Referee: Greg Garner (England)
Assistant referees: Ian Tempest (England), Andrew Pearce (England)
TMO: Trevor Fisher (England)
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!