Franco Di Santo fired the visitors ahead after seven minutes, before Jordi Gomez doubled their lead inside 90 seconds.
Thomas Vermaelen reduced the deficit with a bullet header on 21 minutes, but the second-half onslaught from the shellshocked Gunners never came as the Latics moved five points clear of the relegation zone.
"We can all be very proud of the manner in which we performed," said the Spaniard, whose side had looked doomed at the turn of the year.
"We always had a mental block against top sides, but we got rid of that at Liverpool and have then felt we can compete against anyone.
"We were very good against Chelsea and deserved a positive result, but it was not a good day in terms of decisions - but nobody can argue we did not deserve the points against Manchester United and Arsenal.
"The second half tonight was as good as we have played this season."