The Gunners secured a fifth straight league success by winning 3-0 at the Liberty Stadium, but only after a goalless first half in which the Swans were the better team.
Bafetimbi Gomis wasted a glorious opening after being put clean through on Petr Cech's goal and Swansea should have had a penalty when Per Mertesacker moved his hand to block Gylfi Sigurdsson's free-kick.
But Arsenal were a different proposition after the break and goals from Olivier Giroud, Laurent Koscielny and Joel Campbell saw them keep pace with leaders Manchester City and open up a three-point advantage on third place
"We are very ambitious, very hungry as well and if we play like that we will be in the (title) fight," Wenger told Sky Sports after Arsenal had avenged last season's two league defeats to Swansea.
"In the first half it was difficult, but in the second half we upped our purpose and tempo and had pace in our combinations.
"Once we scored the first goal we were the dominant team and won the game normally."
Giroud's header four minutes after the restart was the 2,000th goal of Wenger's 19-year reign, but the Arsenal manager was more concerned with points than landmarks ahead of this week's testing Champions League visit to Bayern Munich.
"I am proud of scoring goals because people like to come to see football to see people try to play," the Frenchman said.
"But the most important (thing), of course, was the three points - and we have made a little difference with some teams.
"Let's focus on the quality of our game and keep a good balance between hunger, humility and confidence.
"It's a very big week for us as we go to Bayern now and then we play Tottenham at home, but we have some very strong results behind us."
Swansea were trying to force their way back into the contest when Koscielny scored a controversial second goal after 68 minutes.
The hosts cried foul after Koscielny challenged Lukasz Fabianski for a cross which looped into the air - the sort of incident which usually results in the goalkeeper winning a free-kick - but on this occasion ended with the Arsenal centre-half stabbing the loose ball home.
But former Gunners goalkeeper Fabianski admitted he might have done better with Hector Bellerin's deflected cross and taken the decision away from referee Kevin Friend.
"The second goal felt like a goal given away," Fabianski told www.swanseacity.net
"I felt some contact (from Koscielny) but maybe I could have made a different decision and punched the ball - then there wouldn't have been a decision for the referee to make.
"The game could have been different, but we were not able to put the chances away, so it's a disappointing final result.
"But if we take the way we played for 60 minutes into the next game, then we can get the three points against Norwich."
Source : PA
Source: PA