Arsenal appeared to be in complete control at half-time after Olivier Giroud's first-half double had put daylight between themselves and an injury-hit Newcastle side.
Newcastle pulled one back in the 48th minute through Moussa Sissoko and the hosts piled on the pressure in the second half.
Only a superb goalkeeping display from David Ospina ensured that Arsenal ended a week in which they exited the UEFA Champions League on away goals with a victory that kept them within a point of second-placed Manchester City.
Wenger said: "We have played four games in two weeks and three away games at Manchester [United in the FA Cup], in Monaco [in the Champions League] and here [Newcastle] and we've won all three.
"The last 14 minutes were difficult because our legs had gone a little bit and Newcastle played very well in the second half but we had an outstanding second half going forward.
"We had a fluent game by creating chance after chance and in the second half we just had to show different qualities and hang on.
"We are in the fight [for second]. You have seen the game - in every game we need to turn up and fight until the last minute to get the points and that's what we have to do."
Asked about the prospect of overhauling the four-point deficit to leaders Chelsea, Wenger added: "Chelsea have a good security and at the moment I feel they have enough to be quite serene.
"We have Manchester City in front of us but if you look behind us it is tight as well, so the important thing is to win our games. Chelsea have too much security."
