Three months after scoring a hat-trick against Spurs, the England midfielder netted two more goals against them in a 4-1 away win on Sunday, while Viktor Gyokeres also scored twice for the leaders.
Eze went close to joining Tottenham in the summer, only for Arsenal — his boyhood club — to swoop in and sign him instead for Stg 60 million ($A114 million).
Spurs are suffering even more now — Eze's only goals since the start of November have come against them.
It felt like a crucial win for Arsenal, who rebounded after two straight draws which have let Manchester City back in the title conversation.
"After what happened against Wolves and losing two points with the last kick of the game, it was tough," Gunnes boss Mikel Arteta said.
"But that's the beauty of this game."
Arsenal regained their five-point lead but City have a game in hand and still have to host Arteta's team in the league in mid-April.
It proved to be a tough start to life as Tottenham manager for Igor Tudor, who has made a habit of picking up good results early in his tenure at previous clubs.
Not this time, though. Spurs did equalise two minutes after conceding the opener to Eze, but Gyokeres made it 2-1 with a shot from the edge of the area in the 47th.
Eze stretched the lead in the 61st minute and Swedish ace Gyokeres sealed it in the 94th.
"A derby can bring you big motivation but there are other things you cannot change in three or four training sessions. It is impossible," Tudor said.
"With the ball, a lack of confidence is very evident."
Earlier, Alexis Mac Allister just wouldn't give up for Liverpool as they won 1-0 at Nottingham Forest.
After having an 89th-minute goal disallowed following a VAR check, the midfielder then scored again in the seventh minute of added time — and this time it survived a video review — to earn the champions a victory.
Mac Allister first thought he'd scored a goal he knew nothing about after he'd turned his back on a clearance by Forest defender Ola Aina and the ball rebounded off him into the net. Yet VAR spotted it had struck his arm and the goal was scrubbed out.
Still, the Argentine battled on, and scored with virtually the last kick of the game when Virgil van Dijk's header was spilled by Forest goalkeeper Stefan Ortega. Barely six metres out, Mac Allister couldn't miss.
There was a VAR check to see if Van Dijk was offside but the goal was given.
Liverpool stay sixth, level on points with fourth-placed Chelsea and fifth-placed Manchester United, whose game in hand is at Everton on Monday.
With doubts swirling around the future of Crystal Palace manager Oliver Glasner, his team dug out a 1-0 win over bottom club Wolves thanks to a last-minute goal from substitute Evann Guessand.
And it wasn't long ago that Sunderland were the only Premier League team with an unbeaten home record, but they've now lost two straight at the Stadium of Light, this time being defeated 3-1 by Fulham.
With PA.
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