Ralph Hasenhuttl’s lineup equalized just before halftime after Ward-Prowse made up for his earlier error to pick out Jan Vestergaard, who headed home the corner.
Cavani struck two goals as Manchester United staged a remarkable comeback to defeat Southampton 3-2 in the EPL 2020-21 season.
Southampton, which is ahead of Liverpool on goal difference, last topped the English standings 32 years ago when the team won its first three games of the 1988-89 campaign.
Villa seemed out of the game, even after Tyrone Mings made it 4-1 with a header, but scored twice more in stoppage time before running out of time to earn a draw.
Everton, which won its first four league games and drew its fifth against Liverpool last weekend, stayed top of the standings.
Palace fielded a heavily patched-up defense because of injuries to centre-backs James Tomkins, Gary Cahill and Mamadou Sakho and full-backs Patrick van Aanholt and Nathan Ferguson.
Ole Gunnar Solskjaer's men were unable to take advantage of weekend defeats for Chelsea and Leicester to remain in fifth.
England was 35-1 at stumps having faced only 17.4 overs because of light but intermittent rain at Southampton's Rose Bowl, where there were no spectators for a match being played.
The Premier League had wanted all squads to take a 30 per cent pay cut but the move led to a standoff with the players' union.
Tottenham registered a 3-2 win over Southampton in the FA Cup on Thursday.
The Egyptian forward scored a brace against Southampton in the second half on Saturday at Anfield. The Reds boss further said that Salah is a team player.
The Reds kicked off the clash in a great manner as the side dominated the possession and made several attempts to score a goal. However, no goals were scored in the first half.
The victory marked Liverpool's best start to a season since they won eight league games in a row in 1990-91.
Chelsea will meet Manchester United in the FA Cup final after beating Southampton 2-0 in the second semi at Wembley Stadium.
Giroud hopes to have kickstarted his Chelsea career after coming off the bench to inspire an eight-minute turnaround from 2-0 down to win 3-2 at Southampton on Saturday.