Sinner is the only top-four player left in the men's draw following the exits of Novak Djokovic, Carlos Alcaraz and Alexander Zverev.
The world number one now has five Grand Slam titles to her name.
The world number one is just one match away from becoming the first woman to win the tournament in three straight years since Justine Henin in 2007 after a 6-2, 6-4 victory.
Swiatek wrapped up victory after nearly three hours.
In front of a packed centre court crowd Swiatek won her 36th match of the year and became the first woman since Serena Williams in 2013 to win at Madrid and Rome in the same season.
Coming back from 1-3 down in the decider and saving three match points in total, Swiatek claimed a 7-5, 4-6, 7-6 (9/7) victory to secure the Madrid Open trophy for the first time.
On the women's side, Iga Swiatek was made to sweat in her 4-6, 6-0, 6-2 victory over Brazilian lefty Beatriz Haddad Maia, as she dropped her first set of the tournament and needed two and a half hours to reach a second consecutive Madrid semi-final.
Zendaya and boyfriend and fellow actor Tom Holland were among the crowd Sunday as Poland's Swiatek beat Maria Sakkari 6-4, 6-0 to win the prestigious Indian Wells WTA title for the second time.
"Really happy, it's not easy to play the first match, especially the first Grand Slam of the season," said Swiatek, who owns three Roland Garros crowns and another at the US Open.
World number one Iga Swiatek on Monday joined Elena Rybakina in blasting late-night scheduling which wrecked the closing days of last week's Montreal Masters.
Women's top seed Iga Swiatek outclassed Spain's Sara Sorribes Tormo 6-2, 6-0 and Daria Kasatkina thumped Jodie Burrage 6-0, 6-2 to reach the third round before organisers worked to clear the backlog of first-round matches.
Djokovic, 36, has only lost twice at Wimbledon in a decade and began the Centre Court programme with a 6-3 6-3 7-6(4) win over Argentine Pedro Cachin after a 70-minute delay despite the roof being closed as ground staff laboured to dry the turf
The 36-year-old Serb, who has won the last four titles at the All England Club, opens proceedings on Centre Court where he has not lost in 10 years.
Swiatek has now lost only two out of 26 Grand Slam matches since moving to world number one in April last year and the 22-year-old became the youngest woman to bag consecutive trophies at Roland Garros since Monica Seles, who won from 1990-92.
