Serena is the third oldest female Grand Slam finalist in the Open era at 36 years and 291 days.
Rafael Nadal beat Austrian seventh seed Dominic Thiem 6-4 6-3 6-2 to claim a record-extending 11th French Open title on Sunday.
The Swiss defending champion dropped his only sets of the tournament before completing a 6-2, 6-7 (5/7), 6-3, 3-6, 6-1 win over the sixth seeded Croatian in 3hr 3min.
Cilic, the world No. 6 and former US Open champion, won 3-6, 6-3, 6-7 (5/7), 6-2, 2-0 in 3hr 47min on Rod Laver Arena when Nadal retired in pain early in the fifth set.
Roselyne Bachelot was handed a €500 ($600) fine by a court in Paris and ordered to pay €12,000 in damages and legal fees to the serial Grand Slam winner over the allegation.
Roger Federer got one over his old rival Rafael Nadal to win the Shanghai Masters 6-4, 6-3 on Sunday in a showdown between the two best players on the planet.