Lampard was furious with Chelsea's lethargic first half at the Emirates Stadium after they fell behind to Pierre-Emerick Aubameyang's early goal.
The Chelsea boss was so frustrated he changed his side's formation in the 33rd minute, hauling off Emerson and sending on Jorginho.
That switch proved an inspired move as Chelsea gradually took control and equalised in the 83rd minute after Arsenal keeper Bernd Leno's mistake allowed Jorginho to tap in.
Tammy Abraham clinched the points with a cool finish four minutes later as Chelsea cemented their grip on fourth place and ended a dismal run of five defeats in seven Premier League matches.
Lampard and his players were all smiles as they celebrated with Chelsea's fans after the final whistle, but he said the win had been sparked by his stern half-time team-talk and the subsequent exchange that triggered between his players.
"We were so awful for 30 minutes, slow lethargic, nervous. The second half was nothing to do with tactics it was all to do with spirit and desire," Lampard said.
"From my point of view you can accept a missed pass but you can't accept lethargy in a London derby. The players were told that and they delivered.
"I said my piece and it was pretty firm. You can't come here and have nothing about you. We are Chelsea, we can't just roll up.
"The lads started talking and it was a bit aggressive, which was a good thing.
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"We made the change and it got better. We controlled everything in the second half, the fight and desire was there."
Rocked by a dismal Boxing Day home defeat against Southampton, Lampard had questioned himself and his players.
He urged them to use this victory, which came a week after their impressive success at Tottenham, as the springboard for a more consistent run.
"The thing at the moment is you do worry if we are going to score. We needed a mistake to score and that gave us the confidence," he said.
"It will only be a turning point if we show it going forward. We won at Tottenham playing great football and today we showed some fight. If we can put the two together we will have something."
It was a bittersweet afternoon for Arteta, who was encouraged by the way his team dominated the early stages but finished frustrated by their failure to see out the result.
"I'm pleased with a lot of things we trained that actually happened in the game. That shows they are buying into what we are telling them," Arteta said.
"But we have to sustain that for longer periods against a very physical team like Chelsea.
"We were defending much deeper than I like. I'm really disappointed with the way we conceded the goals."
Arteta admitted Leno was feeling low after his blunder and he refused to blame the German.
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"When an error costs a team it is harder. He will be down and we have to lift him," he said.
Arteta felt the key moment was not Leno's mistake, but Jorginho avoiding a red card when he committed a clear foul having already been booked before scoring.
"For me it was very clear, that's it. I prefer not to talk about it," he said.
Lampard conceded Chelsea had been fortunate, saying: "Maybe we got a bit of luck."
Arsenal have now won only one of their last 15 games in all competitions and sit well adrift of the top four.
And Arteta, without a win in his first two matches, admitted the Gunners were far from Chelsea's quality.
"It is tough to match the level that Chelsea play at. It's not that they didn't want to do it or were scared," he said.
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