With the sides tied at 14-14 heading into the last five minutes, Edoardo Padovani’s penalty looked to have secured a first win in the competition this season for the Italians.
However, Aki touched down following a driving maul at the death to secure an important win in Connacht’s bid to chase down Conference B leaders Munster.
The Westerners trailed their fellow Irish province by nine points heading to Italy, with Munster playing Cardiff Blues later on Friday before a meeting with Connacht at Thomond Park next weekend.
Andy Friend’s side owed much of their struggle in Treviso to a costly Shane Delahunt sin-binning late in the first half for a dangerous tackle on Jayden Hayward.
Connacht led 7-0 at the time thanks to Finlay Bealham’s early try, but – with the visitors down to 14 men – Benetton moved in front before half-time through converted tries from Davide Ruggeri and Leonardo Sarto
Paddy McAllister touched down to level up the scoreline once more early in the second half but it was Benetton who kicked on from that point.
However, a rare victory was cruelly ripped from their grasp when Ireland centre Aki found the line with Connacht’s last-ditch effort.
Having come close to touching down moments earlier amid sustained pressure on the Benetton line, Bealham burrowed over in the 16th minute, with Conor Fitzgerald adding the extras.
Connacht were dealt a blow when Delahunt was penalised for lifting Hayward above the horizontal and planting him on his back, earning him 10 minutes in the bin.
The Italians swiftly made their visitors pay when Ruggeri powered his way over next to the posts and Padovani levelled the scores.
Benetton were in front by half-time, spreading the ball out to the left wing, where Sarto expertly stepped back inside to find the gap and showed a tremendous turn of pace to race for the line, with Padovani again on target from the tee.
Connacht emerged for the second half determined to make amends and promptly touched down through McAllister before Delahunt had returned to the field.
Fitzgerald restored parity, but with the game in the balance it was Benetton who finished the stronger and Padovani kicked them into a winning position.
However, Connacht’s decision to kick for the corner from their remaining penalties eventually paid off when Aki produced the winning touchdown.