"One more win and we will be in the top four for sure," Wenger told reporters, while injecting a note of caution. "I’m long enough in the job to know to get over the line is always difficult."
Arsenal, who will face a European side in a playoff to reach the Champions League proper if they finish fourth, opened the scoring in the 26th minute through Laurent Koscielny when he prodded home Santi Cazorla's free kick.
Mesut Ozil then doubled the hosts' lead in the 42nd minute with a tap-in after Tim Krul had twice denied Olivier Giroud.
Arsenal were rarely threatened and added a third after 66 minutes with a powerful Giroud header.
Arsenal's 3-0 humbling at Everton earlier this month looked to have ended their hopes of Champions League qualification but a run of three successive victories coupled with Everton's stuttering form has the Gunners back in the driving seat.
"We have gone through a difficult period and Goodison Park was one of them," said Wenger. "The spirit in the team is strong, determined and healthy and you can see that in the way we have bounced back from disappointment.
"We would love for the season to be longer. We are four points ahead of Everton and we want to take maximum points from now until the end of the season.
"We have shown that we have potential, but we want more,”continued Wenger. "Next season hopefully we can do it, but lets finish well this season first."
DOUBLE SAVE The Gunners dominated possession early on but failed to create any clear chances. When the first goal did come it was through the unlikely source of centre back Koscielny, who got the faintest touch on Cazorla's teasing delivery. Arsenal could have doubled their advantage immediately but the in-form Lukas Podolski was thwarted by Krul twice within two minutes. Ozil did what his German international team mate could not and added a second with a simple finish after Krul had pulled off an impressive double save at the feet of Giroud.
Ozil then turned provider with a wicked cross for Giroud to power in his 15th Premier League goal of the season. Ninth-placed Newcastle had manager Alan Pardew back on the touchline after serving a seven-game ban following his head-butt on Hull City's David Meyler but his presence failed to inspire his side, who have now lost six games in a row for the first time since January 1987.
Supporter unrest is growing against Pardew and his shot-shy side.
(Writing By Tom Hayward, editing by Mark Meadows/Alan Baldwin)
