Orient went ahead through Moses Odubajo after seven minutes and although they missed a penalty when Kevin Lisbie sent his shot wide of the target, the home side were given a second chance from the spot 10 minutes later when David Mooney converted having won the initial foul.
The home side totally ran the show in the first period, but Crewe improved after the break with Chuks Aneke going close to reducing the deficit including an effort that hit the crossbar.
But Orient held out to maintain their 100% record with a fourth successive win that equals a club record set during the 1910-11 season.
"We put on a great performance before the interval and they seemed unable to cope with us," Slade said.
"Inevitably Crewe came back into it in the second period and got a few corners and put us under a little bit of pressure, but we did enough to get the block in and there were also two exceptionally-good saves from Jamie Jones.
"So whoever has been called upon has done a job. We kept a clean sheet and that was important.
"When you've had all the play in the first period and could have been three or four goals up and we've still not put the game completely to bed, you have to expect Crewe to come at you in the second period, but we stood up and that was very satisfying. "
Orient were awarded two penalties by referee Keith Stroud and also had strong claims for another three turned down.
"Any of the five could have been given, but it's difficult for the referee because of the conditions," Slade added.
"But we did feel there was another one in there for sure. Fair play to Kevin Lisbie, he missed a penalty and give up the chance to atone by giving the second one for the sake of the team and David Mooney has taken the opportunity.
"I'm sure there will be a discussion going on in the changing room between the pair of them as to who takes the next one."