(CNN) -

For the serious contenders at grand slams, it's all about trying to advance with minimal fuss in the first week. That way they have plenty of energy left for when the competition picks up in the second week.

Serena Williams certainly isn't messing around in the early stages of this year's U.S. Open.

After crushing Taylor Townsend -- a potentially tricky opponent -- in the first round in 55 minutes, Williams routed another fellow American, Vania King, 6-1 6-0 in 56 minutes Thursday to reach the third round.

Men's No. 1 Novak Djokovic made quick work of his opponent, too, dispatching Paul-Henri Mathieu 6-1 6-3 6-0.

This grand slam is big for Williams.

Even though she has won 17 majors, none have come in 2014 and she didn't progress to the quarterfinals at the Australian Open, French Open and Wimbledon.

But New York could once again bring Williams joy -- she is the two-time defending champion.

The top seed's only problems against King came in her first service game, when Williams hit three double faults in windy conditions.

Williams' path to the final got a little easier when Ana Ivanovic was upset by big-serving Czech Karolina Pliskova 7-5 6-4 and Samantha Stosur -- who defeated Williams in the 2011 final -- blew match points and lost to Estonia's Kaia Kanepi in a third-set tiebreak. Ivanovic and Stosur were in Williams' quarter.

Just how potent is Pliskova's serve? She trailed only Williams in aces heading into the tournament.

Still, it marks more grand slam disappointment for Ivanovic, the eighth seed and a former No. 1.

Despite occupying the final spot in the race for the year-end championships, Ivanovic crashed out early at Roland Garros, Wimbledon and now the U.S. Open.

"I do put a lot of expectations on myself," Ivanovic told reporters. "I tried to overanalyze and overthink instead of just playing the game.

"It's a work in process. But I think I have potential to do well" at grand slams "and that's something I want to change for next year."

Almost forgotten this year is Victoria Azarenka, since she's missed most of 2014 with a foot injury and this month dealt with a knee complaint.

The two-time finalist, however, rallied from a break down in the first set and then cruised past Christina McHale 6-3 6-2.

"It's always going to take time to rebuild," Azarenka told reporters. "I feel like I'm improving day to day.

"I play much better than I played a month ago. So that's important."