The Peruvian playmaker – who scored his first goal in English football against Cheltenham Town last month – fired the League One side in front just five minutes into their Papa John's Trophy tie, with his shot from the edge of the box taking a deflection on its way in.
Ten minutes later, Vilca's through ball allowed Joe Dodoo to make it 2-0, and it was a lead Donny held until the break.
After the restart, Vilca went close to adding his second when his shot cannoned back off the crossbar after 53 minutes.
Dodoo's second of the night made it 3-0 and despite two late consolations from the hosts, Rovers held on to claim the victory to secure their place in the next round.
Jake Turner was also in action on Tuesday, lining up for just the second game of his loan spell at Colchester United as the U's took on Ipswich Town at Portman Road.
Goalkeeper Turner kept a clean sheet, too, as the game finished 0-0.
But despite saving from Joe Pigott in the ensuing penalty shoot-out, Turner still ended up on the losing side as the League Two outfit were beaten 4-3 on spot-kicks.
And Lewis Cass played his part in another memorable win for Port Vale, as he started their 5-0 win over Liverpool's under-21s.
The defender, who netted his first senior goal in the Valiants' 5-1 FA Cup win over Accrington Stanley on Saturday, was withdrawn at half time, with his side leading 2-0.
Photo credit: AH Pix/Doncaster Rovers