And Dave Baikie's side found themselves three down after half an hour when Aluko's rasping shot ricocheted off Greig McDonald and flew past Brown.
Sean Fagan was lucky to avoid another red card when he was seen aiming a punch in the direction of Aluko.
There was little succour for East Fife after the break although the pace dropped as Aberdeen enjoyed the luxury of their substantial lead.
Vidal fizzed a long-range shot narrowly wide of Brown's post. And Brown then pulled off a super save from Scott Severin as the home side pressed for more goals.
Lone East Fife striker Chris Templeman forced Aberdeen keeper Jamie Langfield into a rare stop with the Fifers showing more composure following their tortuous start to the game.
Maguire squandered a golden opportunity to make it four with 15 minutes to go when he latched onto Langfield's long clearance but, with only Brown to beat, the midfielder blasted the ball high over the bar.
The youngster made amends minutes later with the East Fife defence posted missing; Maguire found himself unmarked at the back post and nodded the ball home from Charlie Mulgrew's outswinging corner.
Maguire then wrapped up a convincing win with a fine solo effort as fatigue took its toll on the battling part-timers.
Aberdeen manager Jimmy Calderwood:
"East Fife were unlucky but that's the game; if Sone Aluko had gone through it was a goal and in the rules of the game (Willie McCulloch) had to be sent off.
"The goals were top quality.
"We've had a few bad results against lower league teams but it was a very confident performance today, we knocked it about for fun and had a lot of pace to our game."
East Fife manager Dave Baikie:
"You can't plan for that, to lose your goalkeeper after four minutes and I've had to take Goran Stanic off.
"It's hard enough playing a Premier League side with 11 men but with 10 men it was game over really.
"We lost our shape in that first twenty minutes and they scored three goals.
"I thought in the second half we kept our shape a lot better but I'm just disappointed we lost those two late goals.
"With the lack of match fitness and being a part-time club it was always going to be the case that in the last 10 or 15 minutes fitness would tell."
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