Despite having the greater possession in the first half, Orient failed to test Alex goalkeeper Ben Garrett and paid the price when the home side found themselves two goals down at the interval.
The visitors incisive football at the business end of the pitch proved decisive. On 34 minutes, Jens Janse sent his intended clearance straight into the path of Cooper who struck the ball into the top left corner of the net from 12 yards.
Two minutes later, Crewe were only prevented from doubling their lead when Tom Parkes cleared a shot from Alex Kiwomya off the line but on-loan Chelsea midfielder Kiwomya was to feature in the second goal.
He sent in a sublime cross from the left to the unmarked Davis who was left with the simplest of close-range finishes to extend his side's advantage.
Only an outstanding save in added time from keeper Alex Ciask prevented Billy Bingham from adding to the Railwaymen's lead.
To compound to Orient's misery, winger and substitute Ulrich Nnomo was stretchered off with a leg injury just 16 minutes after joining the action leaving the home side to play out the final few minutes with 10 men.
During the second half, a section of the Orient crowd calling for president Francesco Becchetti to quit the club and the home team left the field to a chorus of boos from the Brisbane Road faithful.
Report supplied by the Press Association.
Substitution, Crewe Alexandra. Tom Lowery replaces George Cooper.
Ulrich N'Nomo (Leyton Orient) wins a free kick in the defensive half.
Foul by Danny Hollands (Crewe Alexandra).
Corner,  Leyton Orient. Conceded by Oliver Turton.
Substitution, Crewe Alexandra. Billy Bingham replaces Ryan Lowe.
Attempt missed. Robbie Weir (Leyton Orient) right footed shot from outside the box is close, but misses to the right.
Oliver Turton (Crewe Alexandra) is shown the yellow card for a bad foul.
Callum Kennedy (Leyton Orient) wins a free kick on the left wing.
Foul by Oliver Turton (Crewe Alexandra).
Substitution, Leyton Orient. Jay Simpson replaces Nigel Atangana.
Substitution, Leyton Orient. Ulrich N'Nomo replaces Gavin Massey.
Corner,  Leyton Orient. Conceded by Oliver Turton.
Jon Guthrie (Crewe Alexandra) wins a free kick in the attacking half.
Foul by Robbie Weir (Leyton Orient).
Delay in match Alex Kiwomya (Crewe Alexandra) because of an injury.
Jens Janse (Leyton Orient) wins a free kick on the left wing.
Foul by Chris Dagnall (Crewe Alexandra).
Attempt missed. Tom Parkes (Leyton Orient) header from very close range is close, but misses to the left.
Corner,  Leyton Orient. Conceded by Ben Garratt.
Attempt saved. Ollie Palmer (Leyton Orient) right footed shot from the right side of the box is saved in the top right corner.
Nicky Hunt (Leyton Orient) wins a free kick on the left wing.
Foul by Ryan Lowe (Crewe Alexandra).
Foul by Gavin Massey (Leyton Orient).
Alex Kiwomya (Crewe Alexandra) wins a free kick in the defensive half.
Second Half begins Leyton Orient 0, Crewe Alexandra 2.
Substitution, Leyton Orient. Michael Collins replaces Jordan Bowery.
First Half ends, Leyton Orient 0, Crewe Alexandra 2.
Goal!  Leyton Orient 0, Crewe Alexandra 2. Harry Davis (Crewe Alexandra) left footed shot from the centre of the box to the bottom right corner. Assisted by Alex Kiwomya with a cross.
Foul by Tom Parkes (Leyton Orient).
Chris Dagnall (Crewe Alexandra) wins a free kick on the right wing.
Ollie Palmer (Leyton Orient) wins a free kick in the defensive half.
Foul by Harry Davis (Crewe Alexandra).
Attempt blocked. Alex Kiwomya (Crewe Alexandra) right footed shot from the left side of the box is blocked.
Goal!  Leyton Orient 0, Crewe Alexandra 1. George Cooper (Crewe Alexandra) left footed shot from the centre of the box to the top left corner.
Foul by Jens Janse (Leyton Orient).
Alex Kiwomya (Crewe Alexandra) wins a free kick in the defensive half.
Foul by Robbie Weir (Leyton Orient).
George Cooper (Crewe Alexandra) wins a free kick in the defensive half.
Robbie Weir (Leyton Orient) wins a free kick on the right wing.
Foul by Chris Dagnall (Crewe Alexandra).
George Cooper and Harry Davis goals earned Crewe Alexandra their first win in seven League Two matches as they beat Leyton Orient at Brisbane Road.