His second, an ice-cool 82nd-minute penalty, killed the contest after Thomas Hitzlsperger's 67th-minute effort had given Villa hope of a point.
Vieira said: "The way Thierry is performing, no-one can stop him. I think he has a good chance of being European Footballer of the Year. He's developed so much since he came here."
"This was a very good team performance. We had no trouble motivating ourselves because we wanted to carry on from what we'd done in Rome.
"They put us under some pressure at 2-1 but we stayed strong and Thierry got his second," added the Arsenal skipper.
Arsene Wenger calls Henry a 'gem' and only the width of a post denied him his second consecutive treble, when his 34th-minute drive bounced out with keeper Peter Enckelman beaten.
Robert Pires slid Arsenal into a 17th-minute lead, shooting low past the Villa keeper after Dennis Bergkamp's pass split the visitorsâ€™ defence.
Darius Vassell posed the biggest threat for the midlaners. His pace embarrassed both Sol Campbell and Pascal Cygan and he forced an early flying save from Rami Shaaban.
Henry netted Arsenal's second four minutes after the interval, when he was fouled by Ulises de la Cruz and got up to bend a perfect free kick past the stranded Enckelman.
Dion Dublin missed with a weak close-range header before Hitzlsperger shocked the Gunners by rattling a 20-yard shot past Shaaban.
But referee Graham Barberâ€™s decision that Steve Staunton had fouled Freddie Ljungberg as they tangled finished Villa.
Henry waited for Enckelman to commit himself, then chipped the ball into the vacant space from the penalty spot.