Bukayo Saka's first-half goal was the difference on the evening, with Rice playing a central role in protecting that lead through 95 minutes of intense pressure from Atletico Madrid.
He made a last-ditch tackle in the second half that proved critical when the tie was still finely balanced, and was central to an Arsenal midfield that outworked and outrun their opponents across the full 95 minutes.
Speaking on the pitch at full-time, Rice pointed immediately to the supporters, whose reception for the team coach on arrival at the Emirates had left every player in the travelling party visibly affected.
"I can't describe it to be honest with you. It's been coming, this night at the Emirates in general. I think it's the best night at the Emirates that I've witnessed — even better than the Real Madrid game last year."
"From the moment we drove in today, the coaches stopped and we thought, what's going on? Because usually we just drive straight in, and the next thing we just see all the flares and the fans and the goosebumps from all the players looking out the window — it was just incredible."
Rice was emphatic about the supporters' contribution to the result.
"I've not seen the Emirates like that. So a big thank you to the fans because we needed that. Even if you're tired, it just gives you that energy to keep going, and I think they played a massive part tonight in making us win."
The England midfielder reflected on what the occasion means for a fanbase that has endured years of near-misses and semi-final exits since the club's last major European campaign.
"This era of Arsenal fans — I know people who have been there from the start have had a lot of ups and downs. But I'm sure this is really up there for them. So I'm happy we've done it for the club and for this set of players and our manager, because everyone deserves it."
Arsenal will play in Budapest on 30 May, facing either Bayern Munich or Paris Saint-Germain. They last appeared in a Champions League final in Paris in 2006, losing to FC Barcelona.
Rice was already looking ahead.
"It's crazy saying that. Bring it on, bring it on — I'll be ready. Budapest, I want every Arsenal fan out there. 200,000 of you, come out. Let's try and do it."
Arsenal remain in contention for the Premier League title and face West Ham United on Sunday.