The 34-year-old American brushed aside Germany's world number 43 Annika Beck 6-3, 6-0 on the back of 25 winners and seven aces and goes on to face long-time Russian rival Svetlana Kuznetsova.
‘I thought it was good. I still want to get out to a little bit of a faster start but I was really focused and calm,’ said Williams, who is just six wins short of Martina Navratilova's Open Era record of 306 Slam wins.
Williams has now won 82 matches at Wimbledon as she remains on course to equal Steffi Graf's Open Era record of 22 Grand Slam titles with her seventh Wimbledon crown.
- Rare middle Sunday play -
Williams took the starring role as play was held on the middle Sunday for only the fourth time in Wimbledon history, and the first time since 2004, as organisers tried to clear the backlog caused by days of rain.
Two-time Grand Slam champion Kuznetsova reached the fourth round for the first time since 2008 despite becoming involved in a row with the umpire over coaching.
The 31-year-old 13th seed battled back from 2-5 down in the final set to defeat US 18th seed Sloane Stephens 6-7 (1/7), 6-2, 8-6.
But the Russian was hit with a code violation for coaching early in the final set which prompted a bitter exchange with umpire Marijana Veljovic.
‘I'm just doing my job,’ said the official.
‘Well, you're not doing it very well,’ responded Kuznetsova, the 2004 US Open champion and 2009 French Open winner.
Russian 21st seed Anastasia Pavlyuchenkova made the last 16 of a Slam for the first time since the 2011 US Open by seeing off Swiss 11th seed Timea Bacsinszky 6-3, 6-2.
Pavlyuchenkova will face US 27th seed Coco Vandeweghe, a quarter-finalist last year, who knocked out sixth-seeded Italian Roberta Vinci 6-3, 6-4.
Vandeweghe is one of the in-form players on grass this year, winning at 's-Hertogenbosch and making the semi-finals in Birmingham.
Russia's Elena Vesnina made the fourth round for the first time in seven years by ending the run of US qualifier Julia Boserup, the world number 225, in straight sets, 7-5, 7-5.
Vesnina will face doubles partner and close friend Ekaterina Makarova, who was a bridesmaid at her wedding last year, for a spot in the quarter-finals.
- Djokovic shock still resonates -
Sunday's programme on Centre Court concludes with German teenager Alexander Zverev facing 2010 runner-up Tomas Berdych.
Tenth seed Berdych is bidding to record his first win against a seed at Wimbledon since 2013.
Zverev, who is through to the third round at Wimbledon for the first time, is hoping to record his first win against a seed at a Grand Slam.
The men's draw is still reeling from Saturday's shock exit of defending champion Novak Djokovic in the third round.
Andy Murray will now be the joint-favourite with Roger Federer to succeed Djokovic.
Murray was not scheduled to play on Sunday but he will take a keen interest in the tie between Australian 15th seed Nick Kyrgios and Feliciano Lopez, the Spanish 22nd seed.
Murray will face the winner of that third round clash which was one set apiece when play was halted for bad light Saturday.
Kyrgios was at the centre of a new row on Sunday when he was heard labelling one of his own support team as ‘retarded’.
The incident, picked up by microphones on Court One, occurred during the second set of his third round match.
His compatriot Bernard Tomic got in trouble for describing himself as standing on court ‘like a retard’ earlier in the tournament.
On Court 12, French 32nd seed Lucas Pouille saw off former US Open champion Juan Martin del Potro 6-7 (7/4), 7-6 (8/6), 7-5, 6-1 in a tie held over from Saturday.
Pouille next faces 19th seed Tomic in what will be his first appearance in the last 16 at a major.
