Hendon’s Casey Maclaren went close on seven minutes as he met a cross, but Jack Turner produced a spectacular save at full stretch to deny him.
Two minutes later, Josh Jackman went on a raid from right-back but he fired wide.
Slough went closer on 20 minutes through James Dobson, who went on a typically strong run before unleashing a shot which beat Tom Lovelock in the Hendon goal, but hit the top of the bar and went over.
Four minutes later, the hosts also hit the crossbar, with Zak Joseph unlucky to see his well-struck free kick clip the woodwork on its way over.
Chris Flood was denied by a combination of Lovelock and a defender and a few minutes before the half time break, Dobson hit a snapshot from 25 yards which bounced back off a post with Flood having a follow-up shot saved.
The woodwork again denied a goal early in the second half, with Joseph seeing a shot deflect off a post, although the striker will be disappointed he didn’t test Turner.
Dobson went close again on 57 minutes as he was denied by Lovelock, but the Slough winger was successful with his next attempt just past the hour mark. Flood went on a powerful run down the left before pulling the ball across for Dobson to beat Lovelock.
Slough looked comfortable with their lead, and could have added to it but Matt Lench was denied by Lovelock from Jackman’s cross.
Looking for an equaliser, Hendon were kept at bay by determined Slough defending, but Dan Uchechi went close with a powerful strike which flew inches over the crossbar after he linked with Murphy.
The post came to Hendon’s rescue yet again two minutes from time as Lench’s effort rebounded back into play, but the hosts eventually cleared the danger.
As the game moved into stoppage time, Hendon won a corner and Lee Togwell cleared only to Arthur Lee, but his shot flew wide.
Slough were then dealt a potentially severe blow as Flood was forced off with a tight hamstring, with Adam Cornell replacing him.
Almost immediately, Niko Muir won another corner kick, and from this one Slough failed to clear, with substitute Kezie Ibe taking advantage to flick the ball home from close range and force a replay.
Hendon Line up
Tom Lovelock, Jake Eggleton, Sam Murphy, Casey McLaren (c) (Dave Diedhiou 68), Rian Bray, Arthur Lee, Daniel Uchechi, Michael Corcoran (Matt Ball 71), Zak Joseph, Niko Muir, Ashley Nathaniel-George (Kezie Ibe 85). Unused substitutes: Harry Wise, Keagan Cole.