A large travelling support swelled the gate at 'The 'Gate' to 320 with most huddled under the cover of the stand as rain fell for much of the first-half at The Coppice.
The Glassboys named an unchanged starting eleven from last Saturday's win at King's Lynn Town, although Callum Powell and Niall Maher were added to the subs bench.
The early exchanges were even with Highgate not afraid to take the game to the visitors.
Stourbridge threatened for the first time with eleven minutes gone. A long free-kick was headed on by Aaron Hayden into the path of Luke Benbow on the right-hand side of the box, but from a tight angle he fired into the side-netting.
Robert Thompson-Brown then tested home custodian Bradley Catlow with a free-kick from just outside the box that drew a diving save from the keeper down low to his right and moments later Luke Benbow sent over a cross from the left, however Hayden directed his header wide.
As the half wore on, the visitors began to assert themselves more. In the 26th minute the home side only half cleared a corner leading eventually to Benbow delivering another cross and this time Jordaan Brown got in a downward header that was saved by Catlow.
Two minutes later Birch stretched to find Greg Mills who struck a low angled shot that Catlow parried away, but in the 29th minute Stourbridge grabbed a deserved lead. Aaron Forde and Luke Benbow linked up to slip Kaiman Anderson in behind Sam Oji and Anderson produced a cool finish under Catlow for his first goal of the new campaign.
As Stourbridge continued to probe, they went close again on 36 minutes. Thompson-Brown feeding Benbow who turned and fired in a shot that Catlow parried.
In stoppage time Aaron Forde chased a ball into the bottom left hand corner and with Catlow drawn off his line to the edge of the area, the Stour midfielder tried to send the ball beyond the keeper towards the unguarded goal, however Catlow managed to make a block to ensure it stayed 1 - 0 at the break.
HT Highgate 0 Stourbridge 1
Conditions were drier for the second period enabling spectators to spread out a bit more around the ground.
Eight minutes after the re-start Mills saw his shot parried by Catlow with Brad Birch unable to capitalise on the rebound.
The Glassboys managed to double their advantage after 54 minutes though. A deep left-wing corner from Mills was met by Hayden ahead of the keeper and his header flew home.
Highgate refused to lie down however and almost found an immediate reply. Lei Brown tried a chipped effort from the left channel area that forced James Wren to make a tip-over save.
Stourbridge hit back with Thompson-Brown playing the ball into Anderson and he in turn found Birch handily positioned in space, however he dwelt on the ball too long and Catlow dived at his feet to gather it.
Robbie Bunn set up an interesting last half-an-hour though when he pulled a goal back in the 61st minute. The hosts were awarded what appeared to be a soft free-kick 20-yards out and Bunn made the most of it with a cracking strike that gave Wren no chance.
Stourbridge suffered a blow on 70 minutes when Mills pulled up suddenly chasing a ball out wide and he was replaced by recent signing Chekaine Steele.
Lifted by the goal Highgate sensed the chance to earn at least a replay and Wren was called into action again in the 72nd minute, saving well down to his right from Marco Adaggio's 25-yard shot.
Leon Broadhurst then replaced Birch a minute later with Callum Powell also entering the fray after 83 minutes in place of Benbow.
With the game opening up in the closing stages as Highgate pushed more men forward, Stourbridge twice worked Catlow. In the 85th minute Thompson-Brown dribbled the ball forward before hitting a low shot that the keeper was equal to and then Powell cut in from the left and took aim, but Catlow got safely behind his effort.
The Glassboys saw out the remaining time to secure a safe passage into the 2nd Qualifying Round with the draw expected to be announced on Monday lunchtime at around 1 pm.
The National League North and South teams will enter the competition at this stage so the likes of Kidderminster Harriers, AFC Telford United, Leamington and Nuneaton Borough will feature in the Glassboys section of the regional draw.
Look out for some coverage of the game and post match interviews on the BBC Midlands Today programme - most likely on Monday evening.
Highgate - Catlow, Wilcock, Pulisciano, Currithers, Oji, Bryan, A Brown, Bunn, Adaggio, L Brown, Batchelor
Subs: Tye, Seabourne, Johnstone, Deards, Revan, Edwards
Stourbridge: Wren, Hayden, Brown, McCone, Pierpoint, Forde, Anderson, Birch, Benbow, Thompson-Brown, Mills
Subs: Steele (for Mills 70 mins), Broadhurst (for Birch 73 mins), Powell (for Benbow 83 mins), Westlake, Hall, Maher (not used)
Stour bookings - Brown, Thompson-Brown and Anderson
Updated 16:28 - 19 Sep 2018 by Nigel Gregg