Williams, 36, missed her home Slam last year, giving birth to daughter Olympia shortly after the tournament started.

Opening Monday's night session at Arthur Ashe Stadium, she won 6-4 6-0 against her 68th-ranked opponent.

The 17th seed will meet Germany's Carina Witthoeft in the second round.

Williams is still on course to meet older sister Venus in the third round, although the prospect of facing world number one Simona Halep - her projected last-16 opponent - has disappeared after the Romanian's shock defeat by Estonia's Kaia Kanepi.

Although she will face tougher challenges, Williams looks well placed to challenge for the record-equalling 24th Grand Slam on the evidence of her victory over Linette.

She put the Pole's serve under pressure in a lengthy third game without being able to convert, going on to break it in the seventh.

After avoiding a brief scare when she was taken to deuce in the following game, she saw out the opening set without facing a break point.

The second set was a different story.

Linette could not cope with her power and accuracy in a 28-minute set, winning just nine points as Williams sealed victory with a 114mph ace out wide.

"It was such a good feeling to be back here - it is one of the best feelings in the world," Williams said.

"The first set was tight, it was my first match back here in New York so it wasn't the easiest.

"Once I got settled I started to do what I've been doing in practise and I felt better.

"I think I'm getting there - I've been feeling great in practice."