Saints' keeper Angus Gunn saved Theo Walcott's penalty and defender Cedric slotted his effort past Maarten Stekelenburg to put the visitors into the last-16 where they will play away at Leicester City.
Champions Manchester City have won their last 10 home league matches scoring a total of 36 goals.
Chelsea lost their 100 per cent Premier League record when London rivals West Ham United held them to a 0-0 draw on Sunday.
Arsenal ended their seven match winless run in the Premier League with a surprise 3-1 London derby victory over Chelsea at the Emirates Stadium on Saturday while Manchester United were held to a 2-2 draw at Leicester City.
Cahill struggled for playing time at club level last year and left A-League side Melbourne City in December to return to Millwall -- where he first came to prominence 20 years ago -- before being released by the Championship club.
Arsenal are eighth, seven points adrift of fourth-placed Chelsea, while Norwich remain second from bottom.
Champions Liverpool are five points clear at the top of the Premier League after a 7-0 away hammering of Crystal Palace while Arsenal's troubles continued with a 2-1 defeat at second-placed Everton on Saturday.
Bilic took over the reins at West Brom in 2019 and was tasked with gaining promotion from the Championship to the top flight.
Joint-leaders Tottenham Hotspur and Liverpool both dropped points on a busy day of English Premier League action as Leicester City and Southampton narrowed the gap in what is shaping up to be one of the most open title races for years.
Liverpool's livewire Sadio Mane scored one goal and played a crucial part in the other as they reclaimed the Premier League's top spot with a scrappy 2-1 win at second bottom Fulham on Sunday.
Manchester United moved three points clear at the top of the Premier League after a Paul Pogba goal gave them a hard-fought 1-0 win over Burnley at a freezing Turf Moor on Tuesday.
Juventus rehire Allegri.
Jota's header earned the three points but it was a struggle in the rain for Juergen Klopp's side who looked uneasy at the back without the injured Virgil van Dijk.
Liverpool dominated the Premier League last season, winning their first domestic league title for 30 years
IMAGES from the English Premier League matches played on Sunday.
Images from English Premier League matches played on Sunday.
Images from English Premier League matches played on Sunday.
Rooney's deal is worth a reported 10 million, meaning he becomes the highest paid player in DC United's history.
IMAGES from the English Premier League matches played on Sunday.
Edinson Cavani and Anthony Martial struck late goals as Manchester United claimed a scrappy 2-0 victory over Everton at a bitterly cold Goodison Park,
'The pandemic has caused football to change a lot, and for the worse. You can see it in the matches, and I hope this all ends soon and we can get fans back into the stadiums and return to normality.'
Chelsea striker Tammy Abraham scored a late opportunist double to secure a 3-0 home win for Chelsea over West Ham United in the English Premier League on Monday.
City were due to open their season against Aston Villa and United against Burnley but those games will be moved.
IMAGES from the English Premier League matches played on Sunday.
Bayern Munich wasted a two-goal lead and needed a lucky 82nd- minute winner from Joshua Kimmich to beat Borussia Dortmund 3-2 in Germany's Super Cup on Wednesday and secure their fifth title of the year.
The defender later became the club's assistant coach before embarking on an eventful career as a head coach, managing Dutch sides Ajax Amsterdam, PSV Eindhoven and Feyenoord plus Premier League sides Southampton and Everton and La Liga's Valencia.
Bruno Fernandes struck from the penalty spot in the ninth minute of stoppage time to give Manchester United victory at Brighton & Hove Albion in the Premier League on Saturday after an incredible finale.
Manchester City's hopes of closing the gap on the Premier League pacesetters were frustrated as they were held to a 1-1 draw at home to lowly West Bromwich Albion on Tuesday.
Real Madrid's French duo Karim Benzema and Ferland Mendy struck in the second half as the Spanish champions overcame an injury crisis to beat Getafe 2-0 at home on Tuesday and close the gap to La Liga leaders Atletico Madrid to five points.
Two late goals by Everton substitutes brought the Merseysiders a third successive win when they beat Crystal Palace 2-0 at Goodison Park in Sunday's only Premier League game.
Two goals from late substitute Olivier Giroud and one apiece by Mesut Ozil and Mikel Arteta secured Arsenal's place in the FA Cup semi-finals with a 4-1 win against Everton at the Emirates Stadium on Saturday.
Arsenal exacted revenge against Liverpool on Sunday, Everton kept a dream alive for their manager and Sheffield United caused a dramatic old-fashioned upset as they all reached the FA Cup quarter-finals.
Leicester City won at Arsenal for the first time in 47 years on Sunday, with substitute Jamie Vardy's late close-range header enough to secure victory in the Premier League at The Emirates.
Everton's Theo Walcott struck just after halftime to secure a 1-0 home win over Newcastle United, on Monday, that took the Merseysiders up to eighth in the Premier League, their highest position this season.
Images from Sunday's action in the Premier League.
Officials were forced to call off the opening day of the first Test between England and the West Indies due to bad light and rain which saw only 17.4 overs being bowled.
The England and West Indies players took a knee in support of the Black Lives Matter movement before the start of play in the first Test at Southampton on Wednesday as international cricket returned after almost four months. Rain delayed the start of the first Test before England captain Ben Stokes won the toss and elected to bat.
Villa's chief executive Christian Purslow said 10 first-team players are among 14 positive cases of coronavirus at the club.
Images from the EPL matches played across England on Saturday.
Dutchman Ronald Koeman has signed a two-year-deal with Barcelona.