The Gunners were 4-2 winners against Spurs in the north London derby at the Emirates Stadium on Sunday afternoon.
Eric Dier and Harry Kane got on the score sheet to cancel out Pierre-Emerick Aubameyang’s opening goal in the derby clash.
However, Arsenal bounced back in the second half to secure three points thanks to goals from Aubameyang, Alexandre Lacazette and Lucas Torreira.
The Gunners managed to hoist themselves above Tottenham and into fourth spot in the Premier League table ahead of their trip to Manchester United on Wednesday night.
Chelsea FC are in third place and a point ahead of Unai Emery’s side in what looks like being an exciting top-four race this term.
Arsenal have failed to secure a spot in the Champions League in the last two seasons to culminate in Arsene Wenger’s exit in the summer.
Former Manchester United defender Neville believes Chelsea FC and Spurs will be worried about Arsenal in the hunt to secure a Champions League spot.
“There’s a real scrap on now [for a top-four finish],” Neville told Sky Sports.
“I thought Arsenal would really struggle to get into the top four, even this morning I thought the next four days would catch them out and would show their limits.
“This [the win over Tottenham] puts them right in the mix because the of confidence and belief they will get out of this game.
“Manchester City and Liverpool are the outstanding two teams and I think they will finish in the top four, but Chelsea and Tottenham will be looking over their shoulder.”
Arsenal appointed Emery as their new manager in the summer and the Spanish head coach made five summer signings to revamp his squad.
The north London side will take on Manchester United at Old Trafford on Wednesday night.
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