"It was definitely very competitive," Williams told reporters. "I expected her to come out and play very well.
"I respect her game. Even though I was leading in the second set she just never gave up."
The high-quality match was close from start to finish, with just one break deciding the first set and three match points needed in the second.
The opening set was effectively decided on a double-fault at 3-2 after Williams had forced a backhand error to set up break point.
Azarenka's second serve was called in but Williams appealed and the Hawkeye line-calling system showed a fault.
Williams had difficulty serving out the set at 5-3, hitting two double-faults and then facing a break point which she saved with a forehand pass.
The American then broke to lead 1-0 in the second set when Azarenka netted a backhand.
A forehand error allowed the Belarussian to level at 3-3 and the set seemed destined for a tiebreak until another forehand pass gave Williams a decisive break for 6-5.
The final point was one of the best of the match, as each ran the other around in a rally before Azarenka strained to hit a forehand that failed to clear the net.
"My serve is a big advantage for me," Williams said. "I (also) think I get a lot of balls back, that helps.
"Off the ground she's very strong and consistent but I think I'm probably a little stronger than her so that helps me to control the point."
Azarenka praised her opponent's accuracy.
"It's not about power," she said. "It's more about precision that she was making it ... close to the lines.
"I had a little bit of bad luck on a few balls but I'm proud of what I did today."
(Editing by Tony Jimenez)