A match played out in an electrifying atmosphere ebbed and flowed before the brothers took charge to carve out a 6-4 4-6 6-3 6-2 victory and give Britain a 2-1 lead.
World number two Andy was inspired, as he has been throughout Britain's run to a first final since 1978, and can deliver the winning point in Sunday's first reverse singles against Belgium's top player Goffin.
Older brother Jamie, the seventh best doubles player in the world, struggled at times, but his nerve proved solid as he served for the match.
When Darcis screwed a forehand wide the brothers embraced and the hundreds of British fans wedged into the claustrophobic 13,000-seat arena in the Flanders Expo roared their approval.
"There was so much noise, it was mental. We were shouting to each other at times but it's brilliant," Jamie said on court as a brass band led a rendition of "We're gonna win the Cup."
"To play in a Davis Cup final with your brother and to win a point for your country is great. We may never get the chance to do that again," Andy Murray told reporters.
"But it's far from over. Obviously to be up 2-1 gives us a better chance of winning. But I'm not getting ahead of myself. I know how good a player Goffin is."
Belgium made a late change to their line-up with world number 16 Goffin replacing Kimmer Coppejans as the hosts' captain Johan Van Herck banked everything on the vital rubber.
On Friday Goffin was a bag of nerves against Kyle Edmund before winning in five sets, but he played superbly from the start on Saturday.
His partner, though, lashed an easy overhead long at 4-5 to give Britain set point which Andy Murray converted with a volley at Darcis's legs.
Jamie dropped serve in the third game of the second set as the Belgians roared back.
Goffin's sharp volley winner with Darcis serving at 5-4 levelled the match and the roars of delight shook the steel rafters hanging low over the illuminated claycourt.
Things swayed towards the hosts when Jamie Murray dropped serve early in the third but the British siblings broke back three times to take the set.
The shaven-headed Darcis was broken again in the third game of the fourth set to put Belgium in deep trouble.
Seven break points went begging for the Belgian duo when Jamie Murray served at 2-1 and with them went the hosts' chance of dragging the match into a deciding set.
Goffin must now beat Murray to keep the match alive, having been thrashed by him three weeks ago at the Paris Masters.
"Tomorrow, I have nothing to lose," he said. "They lead 2-1 in the tie. I just have to give everything I have for the match."
(editing by Justin Palmer and Ian Chadband)
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