Stephen Robinson says St Mirren have "no fear" as they prepare to face Brann after thrashing Valur 4-1 in Conference League qualifying.
Following last week's 0-0 draw in Iceland, the deadlock in the tie was broken in Paisley as Shaun Rooney headed his first Buddies goal and the club's first in European competition since 1987.
Toyosi Olusanya rolled in St Mirren's second and captain Mark O'Hara's superb volley put them well on their way to the next round.
Tryggvi Haraldsson reduced Valur's deficit with a penalty but a late tap-in by Alex Iacovitti - also his first St Mirren goal - rounded off victory for Robinson's side.
Norwegians Brann visit Paisley next Thursday, with the return leg in Bergen the following Thursday.
St Mirren have a first European win in 37 years. Their next aim is secure a second inside eight days.
And Robinson told BBC Scotland: "We worked so hard to get here last year, the boys have worked ever so hard to get into the next round.
"We have no fear. We're going to go and enjoy every minute of it. We've got players that can hurt teams. There's absolutely no reason why we can't get a result.
"I won't get too carried away about the group stages but that's obviously the aim. We've got games before that that'll test the squad.
"We need to be at the top of our game to progress. Can we improve on that performance? I believe we can."
Rooney garnered a reputation for himself with cup final goals for St Johnstone and delivered on the big occasion once again as he rose to head O'Hara's corner powerfully into the net.
Valur almost responded straight away. Haraldsson got into a terrific position but was denied by goalkeeper Ellery Balcombe's fine save.
St Mirren pressed throughout the first half but could not double their lead. However, anxiety was eased in the second period, in somewhat controversial circumstances.
Roland Idowu looked offside as he latched on to a headed knock-on off a long ball and unselfishly passed to Olusanya for a simple finish. No flag and no VAR meant the goal stood.
And the home side's night just kept getting better with the goal of the night.
O'Hara was well positioned at the edge of the box to meet a long throw-in with a perfectly struck volley.
Valur were given a lifeline when Jaden Brown felled Jonatan Jonsson and Haraldsson coolly converted.
But Iacovitti ensured the night ended in rapturous celebration for the St Mirren faithful by scoring on the rebound after Jonah Ayunga's header at a corner had been saved.
Player of the match - Mark O'Hara
The St Mirren captain set up one and scored a stunner himself.
St Mirren deliver on memorable night - analysis
While 0-0 away from home last week could never be regarded as a poor result, the onus was really on St Mirren to force the issue in their home leg and that they did.
An early goal always helps but St Mirren's intent to keep pressing rather than sit back meant Valur never really got a foothold in the match.
Also admirable were St Mirren's fitness levels against a side midway through their season.
Next week presents a stiffer challenge for Robinson's side, with Brann having overcome Dutch side Go Ahead Eagles in their tie, but by then St Mirren will have another 90 minutes under their belt.
What they said
St Mirren manager Stephen Robinson: "It was a really professional performance.
"It's only our second game of the season, there's been seven changes from last year and the boys are still finding their fitness.
"We've worked on our corners tirelessly. We didn't score enough set plays last year, we've scored two tonight and we had plenty more chances. It's nice to see that rewarded."
St Mirren's Shaun Rooney: "We did what we had to do on the night and we're looking forward to the next round. That [performance] was the gaffer down to a T. Everybody was tight together.
St Mirren captain Mark O'Hara: "I'm just taking it all in. It's a special moment but we want more of this. We've got a big game next week and the week after.
"We believe we can beat anyone, especially here. We're confident we can get a result against anyone."
Valur manager Arnar Gretarsson: "Today we didn't match them in physically. They were one or two leagues ahead of us. We couldn't play our game.
"A lot of these guys haven't played in this atmosphere, they were a little bit afraid to play. St Mirren today were better than us."
What's next?
St Mirren open their Scottish Premiership campaign at home to Hibernian on Sunday (15:00 BST).