And the Rebels had to do it the hard way, with captain Mark Nisbet harshly sent off after just ten minutes, leaving Slough to battle on with just ten men for the remainder of the game.
It looked likely that a long, hard afternoon would be in store for Jon Underwood and Neil Baker’s side, but instead Slough put in the kind of performance that led to Baker hailing the result as one of his best in management.
In the first major incident of the match, Nisbet brought down striker Charlie Walker just outside the box after a clever pass from his partner Yemi Odubade. Josh Jackman was close by to provide cover, but referee Dean Skipper decided that Nisbet was the last man and sent him off.
Slough reacted immediately by withdrawing striker Ben Harris in place of Scott Davies, but minutes later found themselves ahead.
Davies played a first-time ball out to James Dobson on the left, and he took little time to play a low ball across the Eastbourne box to Stevens, who had made a storming run, and the striker side-footed past Mark Smith from six yards.
With their very next attack, Slough doubled their lead. Dobson again had time on the left wing to chip in a cross, and Stevens was on hand again from six yards out, this time heading firmly past Smith and into the bottom corner.
Improbably, Slough scored their third with just over half an hour played. Warren Harris slipped in Jackman, who had made an overlapping run, and the full-back was clipped just inside the penalty area by Dave Martin. After consulting with his assistant on that side of the pitch, referee Skipper pointed to the spot and up stepped Dobson to coolly roll home his second spot-kick in as many matches.
Eastbourne went close to getting back into the match when Walker found space in the box to turn and shoot, but Jack Turner was in typically fine form, turning the ball over the bar.
Slough very nearly added a fourth with Dobson’s attempted chip from distance landing just over Smith’s bar, but the East Sussex side were able to pull a goal back before the interval.
Martin crossed in from the left and this time Walker got his head to the ball and sent it into the bottom corner, leaving Turner no chance.
Slough withstood pressure early in the second half, with George Wells and Warren Harris blocking from Kane Wills and Walker respectively.
And on 63 minutes, Stevens looked to have made sure of the three points for Slough, despite his side’s numerical disadvantage.
A long kick from Turner was flicked on in midfield and then again by Dobson, and Stevens beat Sergio Torres to the ball before bearing down on Smith and placing the ball past him to secure his hat-trick.
Eastbourne’s response was immediate, with Marvin Hamilton crossing low for Dean Cox, who found himself with plenty of time and space to pick out the bottom corner of Turner’s goal.
Plenty of pressure then followed from the hosts. Kristian Campbell headed a good chance over the bar and Walker went agonising close as his attempted overhead kick rebounded back off the crossbar.
Turner made another fine save to beat away a fierce strike, and Eastbourne were denied a penalty after Odubade went to ground in the box.
Hamilton smashed a swerving shot over from just inside the box as the game drew to a close, but the ten men of Slough held on and preserved their lead.
Eastbourne Borough Line up
Mark Smith, Marvin Hamilton, Kristian Campbell, Kane Wills, Harry Pollard, Tom Gardiner, Dean Cox, Sergio Torres (c), Charlie Walker, Yemi Odubade, Dave Martin. Substitutes: Mike West, Ryan Hall, Tom Day, Andrew Briggs, Gregor Shaw.