* Williams takes fight to Dellacqua
* Li pulls of escape against Keys
* Radwanska back in top form (Adds late matches)
MIAMI, March 23 (Reuters) - World number two Li Na finally made her first appearance at the Sony Open on Sunday, taming Madison Keys in an unsteady effort while three-time champion Venus Williams was also made to work under a blazing Florida sun for her spot in the fourth round.
Li displayed some signs of rust in her first match of the tournament after receiving an opening round bye and a walkover when Alisa Kleybanova withdrew from their second round meeting with illness.
She had to fight off three set points and an early break in the second set before clinching a 7-6 (7-3) 6-3 win over her American opponent.
Williams, seeded 29th at the tournament she considers her home event, battled Casey Dellacqua for almost two and a half hours before subduing the determined Australian wild card 6-4 5-7 6-4.
Third seed Agnieszka Radwanska of Poland continued to confirm she is over the knee problem that plagued her in the final in Indian Wells last Sunday, registering a 7-5 6-3 victory over Russian Elena Vesnina.
Keys, who lives in nearby Boca Raton, had her Chinese opponent on the ropes several times but allowed the experienced Li to escape time-and-time again.
"She's number two in the world for a reason. She just won the Australian Open for a reason," said Keys. "She's a great player.
"I played well at times and she just played the bigger points really, really well.
"There is a lot to be happy with but there is also some stuff I need to work on."
Li got off to a strong start, grabbing the early break and a 3-1 lead, but the big hitting Keys answered with two breaks of her own, surging in front 5-3.
Keys however could not convert any of her three set points, Li wiggling free with a break and forcing the set to a tie-break which she easily won 7-3.
The American again had Li under pressure in the second, grabbing the early break to go up 2-0, but could not sustain the pressure as Li, having now hit her stride, stormed through the next five games on her way to victory.
"I think it was pretty tough match, she played well, big serve, big forehand, especially when she was 3-1 down and then come back 5-3 up and serve for the first set," said Li. "During that time I didn't think about too much.
"I say, OK try to hit the ball, try to do what you have to do and save the set point.
"I think this maybe changed the match a little bit because after that I was feeling she's dropped a little bit."
Williams was not at her best against Dellacqua committing 44 unforced errors and six double faults but she did not lack for fight in the blistering mid-day sun.
"If I go down it's never easy," said Williams. "At least my opponent knows they have to go to the end of the earth to take me out no matter what the circumstances, usually.
"I do try and compete. I mean, being out here, even if it's not your best day, no matter what the circumstances are."
In other third round action, Slovakia's Dominika Cibulkova, the 10th seed, was a 7-6 (8-6) 6-4 winner over Frenchwoman Alize Cornet. (Editing by Gene Cherry/Greg Stutchbury)