Brazilian midfielder Denilson fired the hosts in front after only five minutes as they looked to leapfrog Manchester United and Chelsea, who do not play until Sunday.
However, Vermaelen was deemed to have been the last man when he pulled down Guillermo Franco, and was shown a straight red card by referee Martin Atkinson.
Arsenal goalkeeper Manuel Almunia, however, saved Alessandro Diamanti's penalty and captain Cesc Fabregas - back from a injury lay-off - made it 2-0 with nine minutes left from the same spot following a handball by Matthew Upson.
"I believe we had an outstanding game," Wenger declared.
"We played with class and spirit and we kept our nerve when the situation became difficult, so overall we have shown a good attitude, good maturity, and in the important moments in any department we were decisive.
"Everybody adapted very well to the situation and technically I believe we were outstanding today."
Wenger was left fuming by Atkinson's decision at the time, which rules Vermaelen out of the next game at Birmingham - leaving Arsenal short at centre-back.
"I felt it was very harsh," he said.
"We have seen this situation so many times in the game without it being punished at all."
The Gunners could, of course, be back down to third should both United and Chelsea, but after another brave display, Wenger's youngsters remain very much in the hunt for a first title since the Invincibles campaign of 2003/2004.
Wenger said: "We are not under any special pressure because we are beyond expectation.
"We want to win the trophy because we are all conscious we have won nothing yet - the hunger is there, the talent is there and I think the nerves are there.
"All we can do is rely on the other results of the other teams, so the only thing we can do is master our own results.
"We have a good chance to do it this year. It will be exciting, tight and the response we gave today in the second half was very important in future games."
West Ham, meanwhile, remain deep in trouble.
Results elsewhere mean the Irons are just three points clear of the relegation zone in 17th place.
Manager Gianfranco Zola felt his side had paid the price for overcomplicating matters .
"I am disappointed, especially after the first half when I thought that we were playing the best game of the season," he said.
"The key was to keep the discipline because you have the extra man and I told them to keep it simple, to move the ball around until we have two versus one.
"We did it for the first five minutes of the second half, but then lost it. We wanted to sort the game out as individuals. You can't think like that.
"With Arsenal, you can expect it will be difficult, even if they are one man down.
"Scoring the penalty would have been a big help because Arsenal would have played different football.
"But they just sat back and played the counter-attack. We just did not use the extra man."
West Ham have also lost to Manchester United and Chelsea in recent weeks.
"Today was a very mature performance from Arsenal," said Zola.
"It is certainly a team who are going to be in contention until the end."
Wolves, a point ahead of the Hammers, come to Upton Park on Tuesday night, before they host Stoke.
Zola said: "Our next two games will tell us a lot, especially the next one when we are playing against a team who are more or less in the same position as us. It will be massive.
"The players did not look like they had lost confidence, they were playing against one of the best teams in Europe and played some good football.
"We will go into the Wolves game in good shape."