The Gunners' 7-3 rout of Newcastle made it four successive victories since being dumped out of the League Cup by League Two side Bradford City.
Central to it all was Walcott's superb display in the striker's role he covets as the 23-year-old opened the scoring in the first half before two brilliant finishes wrapped up the points for the north London side.
The former Southampton star has still to sign a new deal to keep him at the Emirates beyond the end of this season despite being offered improved terms.
But Wenger was clearly impressed by Walcott's display and the Frenchman is confident that an agreement will be reached.
"He's done very well and it just typifies what I think he can do," Wenger said.
"He can play through the middle, I'm convinced of that, and he can only get stronger in there. I believe he has become a good finisher. He has learned a lot because he is an intelligent player and because he is intelligent he will continue to improve."
He added: "The intensity of my desire (for him to stay) is exactly the same as it was before the game. My desire is to extend his contract and I think he belongs here. Hopefully we can do it. I think he loves the club and the club loves him and the reciprocity in love is the most difficult to find."
Walcott shines throughout
Walcott dazzled from start to finish in an entertaining match that once again highlighted the two contrasting sides to Arsenal's season.
On the one hand, their attacking prowess was in full evidence from the very first minute when Alex Oxlade-Chamberlain wasted a decent chance from Jack Wilshere's through ball.
It took until the 19th minute to make the breakthrough as Lukas Podolski picked out Walcott's run and he finished brilliantly past Tim Krul.
But Arsenal's weakness without the ball was shown just before the break as they allowed Newcastle back into the game, albeit via a lucky deflection off Jack Wilshere from Demba Ba's free-kick.
The second half was a flurry of goals and it took just five minutes for Arsenal to re-establish their lead.
Santi Cazorla found Oxlade-Chamberlain on the edge of the area and the youngster picked his spot perfectly.
Newcastle were level again within 10 minutes however, as Sylvain Marveuax tapped home following good work from Gabriel Obertan.
Podolski restored Arsenal's advantage when he bundled home after Wilshere's superb cross caused panic in the Newcastle area but another goal from Ba - his 13th of the season - incredibly made it 3-3.
At that point the game could have gone either way but Walcott was determined to make it his evening.
A precise finish high into the net after a cutback from Kieran Gibbs put his side back in front and Walcott turned provider for Arsenal's fifth as sub Olivier Giroud headed home.
Another goal for the French striker made the points safe but the piece de resistance was left to end for Walcott.
Brought down by two defenders, he regained his footing to execute a delightful chip over Krul and round off a perfect performance.
Magpies fail to find their wings
After losing 4-3 against Manchester United at Old Trafford on Wednesday, it was tough for Newcastle to stomach and manager Alan Pardew admitted Arsenal's extra rest after their midweek fixture with West Ham was postponed had been a crucial factor in their victory.
"We certainly wouldn't have had a scoreline like we had (if Arsenal had played West Ham)," he said.
"I thought when we got back to 3-3 we should have shut up shop. We just couldn't do that. The energy levels between the two teams was evident at the end.
"One team was energised, the other was really leggy and I think the fourth goal knocked the wind out of our sails a little bit. We had conceded a couple of bad goals before that and that's why we ended up with score that we did."