Deeping Rangers will face former Football League club Kidderminster Harriers in the Emirates FA Cup second qualifying round.
The Clarets equalled their best-ever run in the competition thanks to goals from Charlie Coulson, Scott Coupland, Dan Schiavi and Jason Kilbride.
The tie against National League North full-timers Kidderminster is scheduled to be played on September 16.
They went ahead after 11 minutes at Brocton on Saturday through Coulson then took control with a quickfire double around the hour mark.
Coupland’s penalty was followed by Schiavi’s strike but Midland League side Brocton got two goals back, only for Kilbride to finish off Scott Mooney’s assist at the end.
Boss Michael Goode said: “We’re really pleased to get through, even though we were not at our best.
We’re really pleased to get through, even though we were not at our best.Michael Goode
“Brocton would be a good side in our league but we got off to an ideal start.
“We were on top and looking pretty comfortable until a few passes went astray.
“They went more direct and put us under pressure.
“The lads seemed a bit down at half-time but we were happy to be 1-0 up away from home.
“At the start of the second half we pressed the ball much higher and tried to go at them.
“At 3-0 we were in dreamland but we got unsettled with Jonny Clay coming off due to a dead leg. We had five minutes of disruption and looked nervy.
“They put a third player up front and we conceded twice so at that stage, it was all hands to the pump.
“Mooney produced a real moment of class and Kilbride finished it off.
“It’s a brilliant result and we can certainly play better.
“We haven’t been at our fluent best in the last few weeks due to players being ruled out.
“We didn’t play well in the Knockout Cup against Cogenhoe United but it was a good point at Boston Town last week with a clean sheet. Now we can focus on Tuesday night’s game at home to Holbeach United.”