Their resolve, though, never diminished, not even when they found themselves trailing for the second time in the match and with less than five minutes left on the clock. They simply kept going and got their rewards when Euan Ferrie passed wide for Rowe to score in the corner to secure Glasgow’s first win on this ground since the 2015 Pro 12 final and their first over Ulster since 2013.

Their reward should have been home advantage all the way through the playoffs but, as is now widely known, there’s a catch. They will play their quarter-final – against one of Ulster, the Lions or Munster – at Scotstoun on the last weekend of this month and then any prospective semi-final at Murrayfield. Should they win both of those ties then they will be forced out of Scotland due to two concerts being staged at the home of rugby. That could see a return to Belfast or, potentially, a daunting trip to South Africa, although Smith again wouldn’t be drawn on hypotheticals.

“I can’t talk about something that I don’t have,” he told Premier Sports. “There has been talk of here and this is a special place. It’s a nice place for a final to be played.”

Warriors’ win came at a potential cost. As well as Fagerson, George Horne, Gregor Brown and Kyle Steyn all picked up knocks of varying degrees during an attritional contest, although Glasgow at least now have the best part of a fortnight to rest and recover for their home quarter-final.

Ulster have a Challenge Cup final to look forward to now but there was no prospect of them going easy here with their playoff prospects still up in the air. It made for a thoroughly competitive contest. Glasgow scored first. Horne, who was able to continue after treatment, found Macenzzie Duncan who had been switched to openside to accommodate Dempsey, who in turn picked out Sione Tuipulotu. The Scotland captain slid a pass to Stafford McDowall who came crashing through on the perfect line to score.

Brown went off soon after, curtailing his comeback after two months out at just 14 minutes, and Ulster soon had their first try of the night. It went to Zac Ward who came off his wing to beat Steyn before simply accelerating away from the Glasgow defence to score. McBeth became the first man in the sin-bin when he caught Bryn Ward on the head with his shoulder – there was no high degree of danger and it stayed a yellow – but Glasgow continued to push for a try, with McKay stopped just short and the forwards then held up.

Dan Lancaster was again starting at 10 with Adam Hastings suspended but blotted his copybook with a wayward pass inside the Ulster 22 that was picked off by Zac Ward who ran the length of the field to score and give Ulster the lead against the run of play. Back came Warriors, however, scoring twice to end the half back in front. The first went to McBeth who atoned for his earlier sin by creeping over the line after Rowe had been thwarted in the corner, with Horne then brilliantly sniping across for Warriors’ third on the night with the clock in the red.

Glasgow were put under pressure early in the second half when McKay was shown a yellow card for staying too upright as Tom Stewart smashed into him. Warriors survived that spell but then conceded two further tries to fall behind. Mike Lowry’s clever grubber kick created the first for Ethan McIlroy despite Steyn’s best attempt to stop him on the line. McIlroy then had a part to play in Ulster’s fourth on the night, keeping in Nathan Doak’s booming kick allowing Bryn Ward to tee up Jack Murphy to score. Warriors were staring a fourth away defeat of the season in the face but Rowe’s late try – after a long TMO check for earlier obstruction – sealed the win and top spot after 18 demanding matches.

“It’s a tough season,” confirmed Smith. “To stay on top of these teams is a massive achievement from my players’ perspective and the club and the coaches’ perspective. I’m very happy. It’s arguably the toughest competition this year that we’ve ever been part of.”

Teams –              

Ulster: M Lowry, W Kok (E McIlroy 41 mins), J Hume, W De Klerk (J Murphy 52), Z Ward, J Flannery, C McKee (N Doak 41); S Crean (A Bell 41), R Herring (T Stewart 14), T O’Toole (S Wilson 52), H Sheridan (C Izuchukwu 41), C Irvine (L McLoughlin 55), J Hopes, N Timoney, B Ward

Glasgow Warriors: J McKay, K Steyn (R Sutherland 25-31, O Smith 61), S McDowall, S Tuipulotu (B Afshar 71), K Rowe, D Lancaster, G Horne; N McBeth (R Sutherland 41), J Matthews (G Hiddleston 49), Z Fagerson (S Talakai 49), G Brown (E Ferrie 14), A Samuel, A Miller, M Duncan (J Oguntibeju 71), J Dempsey (S Vailanu 52)

Referee: Gianluca Gnecchi (FIR)

Scorers –

Ulster: Tries Ward 2, McIlroy, Murphy Cons Flannery

Glasgow Warriors: Tries McDowall, McBeth, Horne, Rowe Cons Horne 3

Scoring sequence (Ulster first): 0-5, 0-7, 5-7, 10-7, 12-7, 12-12, 12-14, 12-19, 12-21, (h-t), 17-21, 22-21, 22-26

Yellow cards:

Nathan McBeth (Glasgow – 21 mins)

Josh McKay (Glasgow – 44 mins)