The 20-year-old England international has fought his way back from a series of niggling injuries which sidelined him for the whole of last season.
While Wenger will continue to be cautious over the player's recovery management, the Frenchman believes it will not be long before Wilshere is back to his best.
"This is the first time I see him very, very close to the player he is," Wenger of his performance against West Brom.
"We have to see if he has no reaction. It was good to leave at home in midweek (for the Champions League tie at Olympiacos)
to give him a breather from time to time.
"But when he plays at that level, and you are under the pressure we are under to win the games, it is difficult to leave him out.
"Jack analyses his game well and is very demanding with himself, he works hard in training.
"The surprising thing for me is that he is (ahead of schedule). I expected him to be back at his best next year, in February. He looks (almost back to his best) much earlier than I expected him to be."
Arsenal's victory - courtesy of two Mikel Arteta penalties - was a first in four matches.
The Gunners moved back up the table to within striking distance of the top four once again.
However, Wenger knows consistency will be key as Arsenal, who travel to Bradford in the quarter-finals of the Capital One Cup on Tuesday night, look to kickstart their season.
"Unfortunately, there is still some big work to do," he said.