Rice opened the scoring by bending one free kick around the Madrid wall in the 58th minute and sent another into the top corner in the 70th as Arsenal won the first leg of their quarter-final 3-0 at Emirates Stadium on Tuesday (Wednesday AEST).
In Tuesday's other quarter-final, Inter Milan won 2-1 at Bayern Munich.
With Madrid great Roberto Carlos looking on in the stands, Rice put on a display of power and bend reminiscent of the many free kicks scored by the Brazilian defender in his day -or by his teammates David Beckham, Zinedine Zidane and Figo for that matter.
Unlike those names, Rice has not been known for his free kick prowess - until now.
"It's been in the locker, but I've hit the wall too many times or it's gone over the bar," Rice told broadcaster Amazon Prime.
"Originally we were going to cross it, and then I've just seen the wall and the goalkeeper's position, so I thought just go for it."
Mikel Merino added the third in the 75th minute to put Arsenal on the brink of returning to the semi-finals for the first time since 2009.
Making matters worse for Madrid, key midfielder Eduardo Camavinga was sent off for a second booking in the final minutes and will miss the return leg at Santiago Bernabeu stadium on April 16.
Kylian Mbappe had Madrid's best scoring chance in the 31st minute when he was played through on goal by Jude Bellingham, but the forward was denied by Arsenal goalkeeper David Raya.
It was the teams' first meeting since 2006, when Arsenal eliminated Madrid in the round of 16. That was also the last time Arsenal came close to winning the competition for the first time, losing the final to Barcelona.
Arsenal delivered one of their best performances of the season against a team that has won the Champions League six times since 2014.
And for once in this competition, 15-time European champions Madrid simply didn't have an answer.
Meanwhile, Inter Milan's treble chances are still very much on after they won 2-1 at Bayern Munich to inflict the German team's first home defeat in the competition in four years.
Lautaro Martinez scored in the first half, shortly after Harry Kane had hit the woodwork for Bayern in an uncharacteristic miss that had the England forward clutching his face in disbelief.
Substitute Thomas Muller, who announced on Saturday that he was leaving the German club at the end of the season, appeared to have rescued a 1-1 draw for Bayern with the equaliser five minutes from time, but Davide Frattesi scored the winner three minutes later.
"Tonight wasn't a walk in the park and we weren't expecting one," Muller told broadcaster Prime Video. "We had a fair few chances, but unfortunately the last counter makes it 2-1."
The result ended Bayern's 22-match unbeaten home run in Europe - a streak stretching back to April 7, 2021, against Paris Saint-Germain - and kept up Inter's hopes of returning to the same stadium for the final on May 31.
But first up they face Bayern in the return leg next Wednesday at San Siro, with the winners playing either Barcelona or Borussia Dortmund in the semi-finals.
