The Bombers conceded only 36 points as they broke their previous record winning margin against the Demons and also booted their highest score against them.
"In years gone by we've probably resorted back to old habits (when we've had a big lead), but tonight we didn't and that was great," Zaharakis told AFL.com.au.
"The coaches just said to play the way that we want to play and not go away from it.
"In Adelaide (in round one) it was great. We played four quarters of our brand of footy, and tonight we didn't go away from the style of footy that we like to play.
"We just wanted to win every contest, get the ball in deep and stick to that all night."
Demon co-captain Jack Grimes is wrapped in a Bomber gang-tackle at the MCG on Saturday night. Picture: AFL Media
Coach James Hird was similarly proud of Essendon's performance.
"Probably except for the last five or six minutes, when the game deteriorated and a lot of players were cramping, the game was played the way we wanted to play," Hird said.
"We wanted to play a defensive style of football that means the opposition can't score, and that happened tonight for us."
Zaharakis was one of the shining lights for the Bombers during the first three quarters of the game.
The 23-year-old, who had an interrupted pre-season after straining his quad in January, collected 26 possessions before being subbed out of the game just prior to the last change.
"I felt pretty good – probably the best I've felt since I did my quad," Zaharakis said.
"I got a quarter in Adelaide, and felt pretty good, then started tonight and played two-and-a-half quarters.
"I didn't know whether I was going to be subbed off or anything.
"But at the end of the third quarter 'Hirdy' said that because of our six-day break, the big game next week and my track record over the last couple of months he wanted to rest me up a bit.
"Hopefully I'll play a full game next week."
The Bombers will need all hands on deck for their match against fellow unbeaten team Fremantle at Patersons Stadium on Friday night.
"Going to Freo to play Freo in the form they're in is as tough a task as you'll get interstate at the moment, so we're under no illusion that it's going to be a big game," Hird said.
"I think we know what we're up for. We watched Fremantle today, and they were excellent in the way they defended the ground.
"Our players know what they're in for. We'll find out whether we're ready when the game starts.
"It's a big game for both clubs."
