The lively Moses Odubajo raced onto a pass from debutant Jamar Loza to fire Orient in front in the 27th minute.
Then, after Tom Eaves squandered a golden chance to equalise for the struggling hosts, the Londoners added a late second with defender Scott Cuthbert credited with getting the final touch to a Dean Cox corner.
"It was very important to us and I think you saw that through my players how important it was," said a delighted Slade.
"What's next is Carlisle, that's all I can tell you. We'll look forward to that and we're back at home for the first time in a while."
Slade handed debuts to Loza, a striker on loan from Norwich, and goalkeeper Eldin Jakupovic, borrowed from Hull, as Orient sealed a ninth away win of the season.
"We've had a lot of away fixtures recently so to pick up three points at a difficult place on a difficult surface was really, really pleasing," he stressed.
"The first goal was really well worked. The interplay between Loza and Odubajo was excellent.
"I don't think any manager feels comfortable at 1-0. Shrewsbury came at us in the second period. We looked as if we might put the game to bed a little bit earlier in terms of counter attacking them.
"But fortunately we managed to get another goal with about five minutes to go which wrapped it up really."