Zaha followed up his stunning strike for the Ivory Coast against Russia last week with another fine goal on Saturday after receiving the ball with his back to the net, turning and driving in a low shot past Thibaut Courtois.
The goal - Zaha's sixth Premier League goal of the season - restored parity for Palace before the forward then set up Christian Benteke for the winner just two minutes later.
After the 2-1 victory, Palace boss Allardyce was full of praise for Zaha and said he believes the 24-year-old is beginning to realise his potential on the pitch.
"Wilf must feel really good about himself," Allardyce said. "His performances are consistent at the moment and he certainly showed it today with his quality of football in possession.
"There's a man on the other side that's an outstanding individual like Wilf, and that's Hazard.
"I think his ability is something that Wilf can look at and try to match.
"But he's already realising his potential by the way he's playing. The potential's becoming a reality."