The Quakers dominated the first half chances in front of a packed Blackwell Meadows but the Saddlers defence stood firm and defender well against high crosses into the box.
Despite winning the midfield battle for most of the match and after failing to take their chances, Caolan Lavery struck just before the 70th minute mark to give Walsall the lead.
The striker met a Rory Holden corner and it was enough to put Walsall into the next round.
Darrell Clarke made two changes to the team that won 2-1 against Cambridge on Saturday, starting in a 4-2-2 formation.
Gary Liddle replaced Alfie Bates in the midfield, while Cameron Norman started in right-back in place of Shay Facey, who wasn’t involved in the squad.
Compared to the team that drew 2-2 at home to Darlington, Clarke made eight changes to the starting XI.
Alun Armstrong’s Darlington made one change to the side that travelled to the Black Country, starting in a 4-3-3 formation - but only naming six substitutes.
Michael Liddle came into the starting XI, replacing Jordan Watson.
The Quakers came into the game on the back of a 5-1 thrashing away at Brackley Town in the National League North.
It was a slow start to the game in front of a loud and full Blackwell Meadows - where Walsall dominated possession of the ball.
Neither side fashioned a chance, however, until the fifth minute. A Darlington attacker was played through down the right and his low cross was aiming for Stephen Thompson but James Clarke slid in well to intercept.
The home side, buoyed by their loud support, almost scored minutes later through Thompson. The ball popped up to the forward in the box, around 10 yards out, but his strong shot was straight at Liam Roberts who stood firm.
Josh Gordon had a good opportunity shortly after. Callum Cockerill-Mollett superbly won the ball back in his own half and fed the striker down the left channel. Gordon cut inside and his shot from the edge of the box was just high over the bar.
Despite his chance, Gordon - alongside Lavery and Wes McDonald - were all struggling to get on the ball against a resolute Darlington defence.
Will Hatfield and Omar Holness were enjoying plenty of the ball through the middle of the park, with Gary Liddle and Liam Kinsella struggling to stop them supporting Thompson up front.
Several dangerous crosses were swung into the Walsall box but Mat Sadler and Clarke defender everything in the air well, to keep the scores level.
The half came to a close with Darlington by far the better side, dominating the attacking possession and limiting the Sadders to long balls up field.
Walsall started the second half with more intent, but still looked vulnerable in midfield.
The first opportunity came within the first five minutes when Norman struck a free-kick, from 25 yards, that sailed over the bar.
Both sides began to fashion chances and just before the hour mark, Lavery went close. An effective Saddlers counter attack saw Holden release Gordon down the right and his low cross was just turned over the bar from Lavery, who was sliding in.
Bates’ introduction, in replace of Liddle, gave the Saddlers more impetus from midfield as they looked to get a foot on the ball against a battling home side. It also saw Holden play more centrally, with the full-backs looking to get further forward.
After a quiet period, the breakthrough finally came in the 68th minute. An inswinging corner from Holden was met by Lavery who rose highest to head home in front of the travelling fans.
Walsall looked to hold onto their lead when they made their final change in the 82nd minute. Defender Dan Scarr came on for winger McDonald.
Although their fans cheered them on until the final whistle, Darlington failed to create a clear chance in the closing minutes as Walsall progressed to the second round of the FA Cup.
They now play League One Oxford in the second round in a home tie to be played at the end of November.
Walsall: Roberts, Norman, Clarke, Sadler, Liddle (Bates 59), Cockerill-Mollett, Holden, Kinsella, McDonald (Scarr 82), Lavery, Gordon (Gaffney 79).
Subs not used: Rose, Jules, Hardy, Adebayo.
Darlington: Connell, Hedley, Liddle, Wheatley (Laing 80), Storey, Galbraith, Rivers, Hatfield, Campbell, Holness, Thompson.
Subs not used: Elliot, Armstrong, Stansfield, Morrison, Watson.
Attendance: 3,006 (105 away).