Li, the Australian Open champion, survived two set points by Flipkens, and eventually took the tiebreaker to avoid another surprise first-round exit like last year. Li goes up against fellow Chinese player Zheng Jie next.
Bouchard, Li's opponent in the Australian Open final, came out on the losing end of a tough match against third-ranked Radwanska, as the Polish player earned her 25th match win of the season.
"The tiebreak was the biggest key," said Radwanska, who goes on to play Svetlana Kuznetsova. "I did a couple of good shots in the tiebreak and managed to win that, and that gave me more confidence in the second set."
Kuznetsova held off Alize Cornet of France 6-3, 4-6, 6-1 as the Russian continued her good run, including reaching the final in Portugal on Saturday.
Also, Caroline Wozniacki was a 6-2, 6-2 victor over Ekaterina Makarova while Spanish player Carla Suarez Navarro followed up from winning her first career title in Portugal with a 7-6 (6), 6-4 win over Yvonne Meusburger of Austria. Ninth-seeded Dominika Cibulkova of Slovakia was bounced 6-4, 6-0 by Samantha Stosur of Australia.
A minute's silence was scheduled to be held at the Magic Box's Manolo Santana center court before the evening match in remembrance of Elena Baltacha, a former top-50 British women's player who died of liver cancer on Sunday.
Nishikori said working with former French Open champion Michael Chang boosted his confidence on this surface as he won his first career clay title in Barcelona.
"I'm playing well and did well last week in Barcelona and I'm getting better on clay so hopefully I can go further this week," the 12th-ranked Japanese player said. "There was just one bad game, on my serve at 3-2 in the second set. Otherwise, it was an almost perfect match."