They went in front on eight minutes when a superb Lloyd James free-kick was headed back across goal and Jordan Moore-Taylor poked home the loose ball from close range.
The Grecians, who lost striker Reuben Reid in the warm-up, then saw Ollie Watkins limp off injured and as they struggled to regroup, George Cooper curled a long-range shot off the top of the crossbar for Crewe.
Exeter were indebted to Christy Pym, who made an astonishing double save to deny Cooper and keep their lead intact.
Two minutes later, it was 2-0 as David Wheeler headed in from close range from Liam McAlinden's 58th-minute cross to make it a club-record seven goals in seven successive matches.
Simpson laid the ball off to Wheeler and he drilled a brilliant 20-yard shot into the bottom corner for the third on 68 minutes.
Crewe's misery was compounded by a straight red card for substitute Charlie Kirk for an awful tackle on Exeter's Jake Taylor and on 86 minutes, James curled in the fourth from 25 yards.
Report supplied by the Press Association
Match ends, Exeter City 4, Crewe Alexandra 0.
Second Half ends, Exeter City 4, Crewe Alexandra 0.
Luke Croll (Exeter City) wins a free kick in the attacking half.
Foul by Jordan Bowery (Crewe Alexandra).
Attempt missed. Jordan Bowery (Crewe Alexandra) right footed shot from the centre of the box is too high.
Goal!  Exeter City 4, Crewe Alexandra 0. Lloyd James (Exeter City) right footed shot from outside the box to the bottom right corner.
Attempt missed. Chris Dagnall (Crewe Alexandra) left footed shot from the left side of the box is close, but misses to the right.
Substitution, Exeter City. Joel Grant replaces Ryan Harley.
Jake Taylor (Exeter City) wins a free kick in the defensive half.
Charlie Kirk (Crewe Alexandra) is shown the red card.
Foul by Charlie Kirk (Crewe Alexandra).
Attempt saved. Robbie Simpson (Exeter City) right footed shot from the centre of the box is saved in the centre of the goal.
Foul by Ryan Harley (Exeter City).
(Crewe Alexandra) wins a free kick in the attacking half.
Corner,  Exeter City. Conceded by Ben Garratt.
Substitution, Exeter City. Luke Croll replaces Jordan Moore-Taylor because of an injury.
Delay in match Jordan Moore-Taylor (Exeter City) because of an injury.
Substitution, Crewe Alexandra. Charlie Kirk replaces Danny Hollands.
Corner,  Crewe Alexandra. Conceded by Lloyd James.
Attempt saved. Jordan Bowery (Crewe Alexandra) header from the centre of the box is saved in the top right corner.
Jake Taylor (Exeter City) wins a free kick in the attacking half.
Foul by Jordan Bowery (Crewe Alexandra).
Corner,  Crewe Alexandra. Conceded by Jordan Moore-Taylor.
Corner,  Crewe Alexandra. Conceded by Troy Brown.
Attempt blocked. Callum Cooke (Crewe Alexandra) right footed shot from outside the box is blocked.
Corner,  Crewe Alexandra. Conceded by David Wheeler.
Goal!  Exeter City 3, Crewe Alexandra 0. David Wheeler (Exeter City) right footed shot from the centre of the box to the bottom left corner. Assisted by Robbie Simpson.
Substitution, Crewe Alexandra. Chris Dagnall replaces Alex Kiwomya.
Foul by David Wheeler (Exeter City).
Ben Nugent (Crewe Alexandra) wins a free kick in the attacking half.
Corner,  Exeter City. Conceded by Zoumana Bakayogo.
Craig Woodman (Exeter City) wins a free kick in the defensive half.
Foul by Callum Cooke (Crewe Alexandra).
Goal!  Exeter City 2, Crewe Alexandra 0. David Wheeler (Exeter City) header from very close range to the bottom left corner. Assisted by Ryan Harley with a cross.
Corner,  Crewe Alexandra. Conceded by Troy Brown.
Attempt missed. Callum Cooke (Crewe Alexandra) right footed shot from outside the box is close, but misses the top right corner.
Corner,  Crewe Alexandra. Conceded by Christy Pym.
Attempt saved. George Cooper (Crewe Alexandra) left footed shot from the centre of the box is saved in the bottom right corner.
Attempt saved. George Cooper (Crewe Alexandra) right footed shot from the centre of the box is saved in the bottom right corner.
Attempt missed. Robbie Simpson (Exeter City) header from the centre of the box is close, but misses to the right.
Exeter City made it 12 games unbeaten with a ruthless demolition of 10-man Crewe at St James' Park.