Brown was originally a travelling reserve for the final against the Bulls in Pretoria, but the back-five forward received a late call-up after Max Williamson went down with a migraine.
Brown came on for Richie Gray after 60 minutes, just before Huw Jones scored the try that put the Warriors in front for the first - and decisive - time. The 23-year-old Aberdonian was then part of a huge defensive effort from the Warriors which kept out the Bulls in the closing stages, and sealed the victory with a maul turnover on the line with the clock in the red.
Brown was right in the middle of that last maul, lifting his head from the pile of bodies to see Stafford McDowall sprinting from the touchline and into his arms to start the celebrations.
"It was all quite funny how it went," Brown told The Times at the Scotland team hotel in Ottawa, the Canadian capital where he hopes to make his Test debut on Saturday night.
"Me, Ross [Thompson] and Murphy [Walker] had gone across to one of the cafes to grab a milkshake. We'd come back to the team hotel and were watching the South Africa game [against Wales, on TV]. My phone popped up with Franco Smith's name.
"At first, I just thought he was going to ask me to run water for the game, but he kind of let me know that I might be in, so I went straight to refreshing myself on all the plays and the lineouts.
"Just as we were going out for the warm-up, it was confirmed that I was going to be on the bench. He phoned me about an hour before we walked across to the stadium, and it was just before the warm-up that it was confirmed.
"It was a really weird feeling, right at the last minute having to get into that mode of being about to play a game. But it might have been a good thing, not being able to stress about it for the week leading up to it.
"After our first trip to South Africa, when we didn't get the results we wanted to, we had a discussion as a group. 'If we want to win this thing, what better way to do it than away from home?' We didn't know at that point it was going to be at Loftus, but we got our heads round the general principle.
"The final probably got a bit tighter at the end than we wanted it to, but there's no better way to win the championship than defending a maul on your own five-metre line and getting the turnover.
"When we're playing and when we feel like ourselves, at the top of our game when everything is flowing, I honestly think we are really hard to beat and definitely one of the top teams out there.
"We had confidence and Franco [Smith, the head coach] spoke about it a lot, that if we brought the best of our processes and stuck to those processes, the outcome would look after itself.
"Even looking at that last maul, it was maul D that we'd done all year, we'd had our roles absolutely nailed down. Coming into the 82nd minute in the final, that showed that everyone knew what they were doing, and we managed to execute it."