Marco Asensio entered the game at the start of the second half and scored less than two minutes in before adding another in the 56th minute.
Real Madrid coach Zinedine Zidane said his side's third successive Champions League title was "something crazy" after the Spanish giants defeated Liverpool 3-1 in Saturday's final in Kiev.
Gareth Bale came off the bench to score twice, including a stunning overhead kick with his first meaningful touch, as Real Madrid ran out 3-1 winners over Liverpool to secure a 13th European Cup in Kiev.
Madrid are the first team to achieve the feat since Bayern Munich in 1976. This is their fourth title in five years, and their 13th overall.
Real Madrid's final Champions League rehearsal was running perfectly on Saturday until Cristiano Ronaldo was substituted and Villarreal scored twice to snatch a 2-2 draw.
Gareth Bale pushed his case for a starting spot in the Champions League final vs Liverpool in Kiev in two weeks' time with two first-half strikes.
Isco scored one and set up another a comfortable victory against Malaga for a much-changed Real Madrid side.
Marco Asensio, Lucas Vazquez and Isco all started ahead of Bale across the two legs against PSG.
Cristiano Ronaldo was rested and the supporting cast failed to show up as Real Madrid endured a shock 1-0 defeat away to Espanyol on Tuesday.
The Welsh international is set to marry his long-time girlfriend Emma Rhys-Jones and reports suggest that the couple want Beyonce to entertain their guests.
Gareth Bale has featured in just 24 matches since signing a lucrative new six-year contract with Real Madrid over a year ago.
Gareth Bale had received stinging criticism from the Spanish press and Madrid fans for his underwhelming displays in Ronaldo's absence in recent weeks as Real dropped points at home to Valencia and Levante.
Cristiano Ronaldo has now struck 12 times in his last six Champions League games.
Gareth Bale moved to the Spanish capital from Tottenham Hotspur in 2013 for a then world record fee of 100.8 million euros.
Gareth Bale, who came on as a substitute on Saturday after three months on the sidelines, scored seven minutes from time as Real Madrid defeated Espanyol 2-0
Zinedine Zidane replaced Cristiano Ronaldo 18 minutes from full-time with Real Madrid leading 2-1
After three matches, Real Madrid lead La Liga standings with nine points and face Espanyol next, who are 15th with two points
Cristiano Ronaldo's free-kick levelled the game in normal time before Alvaro Morata met James Rodriguez's cross deep into stoppage time to complete a dramatic fightback from Real Madrid