Emery’s team extended their unbeaten run to 19 matches in all competitions after fighting back from 2-1 down in arguably the Premier League’s game of the season so far.
Pierre-Emerick Aubameyang’s penalty had put Arsenal ahead before Eric Dier’s header and a Harry Kane spot-kick gave Tottenham the lead at half-time at the Emirates Stadium.
Dier’s gloating celebration had triggered a touchline brawl involving Arsenal substitutes.
But the fireworks were far from over as Aubameyang’s superb long-range equaliser sparked a second half surge from the Gunners.
Alexandre Lacazette came off the bench to put Arsenal ahead and Lucas Torreira sealed the points with his first goal for the club.
Capping a miserable day for Jan Vertonghen, the Tottenham defender was sent off in the closing stages after earlier giving away Arsenal’s penalty.
“It is a very big match for our confidence. Now we have to continue our process,” Emery said.
“It is a very big victory. We give this to our supporters because it’s a very special match against Tottenham.”
It was only Arsenal’s second win in the last nine league north London derbies and, while stealing local bragging rights is always sweet, this felt like a significant moment for Emery’s team in the bigger picture.
Emery has revived Arsenal since the depressing final years of Arsene Wenger’s reign.
But losses to Manchester City and Chelsea and a draw with Liverpool had raised questions about Arsenal’s ability to compete for a top four finish.
This stirring comeback was exactly the kind of statement Arsenal needed as they moved above Tottenham into fourth place on goal difference.
Ending their hated neighbours’ six-match winning run showed Arsenal aren’t content to let the balance of power in north London remain with Tottenham.
But Emery warned his side not to get carried away with another big test looming at Manchester United on Wednesday.
“We are happy and enjoying. But Tottenham beat Chelsea but then they lost to us. That is a big example for us as we think about the Manchester United match,” Emery said.
“We know it is very difficult in Manchester. We are going to prepare as best we can. It is a big challenge for us.”
Tottenham boss Mauricio Pochettino admitted his players suffered mentally and physically at the end of a draining week that included vital victories over Chelsea and Inter Milan.
“It was complicated from the beginning of the game. After the third goal it was tough to come back mentally, to find the energy to go again,” he said.
“We started to feel the effort we made in the Champions League and the Chelsea game. It was a big week.”
Biting into challenges and harrying Tottenham into panicked mistakes, Arsenal made a blistering start and their relentless tempo paid dividends in the 10th minute.
Vertonghen jumped with Shkodran Mustafi as they challenged for a corner and the Belgian’s raised arm clearly made contact with the ball as he tried to block the Arsenal defender’s header.
– Fever pitch –
Referee Mike Dean awarded a penalty and Aubameyang sent Hugo Lloris the wrong way from the spot for his 11th goal of the season.
Tottenham snatched a 30th minute equaliser as the derby reached fever pitch.
Christian Eriksen’s inswinging free-kick caught Arsenal captain Granit Xhaka flat-footed and Dier nipped in to head past Bernd Leno’s weak attempted save.
Dier celebrated by holding his finger to his mouth to indicate the Arsenal fans should keep quiet.
Arsenal substitutes Stephan Lichtsteiner and Aaron Ramsey took exception to Dier’s taunting, prompting a bout of pushing and shoving.
Son Heung-Min’s pace was too much for Arsenal to handle and Rob Holding responded by making a rash sliding challenge on the South Korean four minutes later.
Kane lashed home the resulting penalty for a record-equalling eighth Premier League goal in north London derbies.
Arsenal’s sense of injustice spurred them on and Emery responded by sending on Ramsey and Lacazette, back from a groin injury, at half-time.
They proved inspired moves as Gabon forward Aubameyang conjured a majestic equaliser in the 56th minute.
Tottenham had reverted to their earlier timid performance and Arsenal went ahead in the 74th minute when Lacazette’s shot deflected in off Dier.
Torreira delivered the knockout blow three minutes later and there was still time for Vertonghen to see red in the 85th minute.