Steven Reid was controversially adjudged to have tripped Santi Cazorla in the box by referee Mike Jones, allowing Mikel Arteta to fire home to put the home side ahead in the 26th minute.
Arsenal then made the three points secure when Arteta converted another penalty in the 64th minute after Alex Oxlade-Chamberlain was brought down by Chris Brunt to seal the north Londoners’ first league win in four games.
Asked if his side were fortunate being awarded the first penalty, Wenger told BBC Sport: “A little bit yes. I spoke to [Santi] Cazorla and he said he [Steven Reid] tapped him.”
He added: “Overall, we played well, created chances and kept a clean sheet. There was no room for dropping any points and I feel it is a positive day. It would have relaxed me [if we had taken our chances]. We were a bit nervous when we had chances because our backs were to the wall.”
West Brom boss Steve Clarke was furious with Jones’ decision to award the first spot-kick and felt his side should have had a penalty of their own.
“I think we were hard done by,” he said. “There was clear daylight between Steven Reid and Santi Cazorla for the first penalty. There was a penalty for us for a Per Mertesacker handball but he gave a free-kick the other way.
“It was the easy way out when you come to a big stadium and the crowd are on your back.”