Leicester moved back to the top of the table - three points ahead of Arsenal, who host Chelsea on Sunday - after they beat Stoke 3-0 at the King Power Stadium.
Charlie Austin netted with his first touch in a Southampton shirt as a 1-0 victory for Saints piled the pressure on beleaguered Manchester United manager Louis van Gaal.
United supporters once again vented their anger towards Van Gaal after watching their team put on yet another dull, uninspiring performance at Old Trafford.
Boos rang out around Old Trafford at half-time and following the final whistle as Saints recorded only their second win at United's home since 1988, but also their second in 13 months.
There was no doubting who the home supporters blamed for this latest insipid display. Van Gaal was jeered at as he walked down the tunnel.
Adam Lallana's last-minute strike gave Liverpool an astonishing first Premier League win of 2016 in a 5-4 success at Norwich.
Jurgen Klopp's men had trailed 3-1 with under 30 minutes to go, then led 4-3 before Sebastien Bassong's stoppage-time strike levelled matters.
But there was still time for substitute Lallana to send a shot into the ground and secure a famous victory as Liverpool's own defensive failings were eclipsed by Norwich's at Carrow Road.
Klopp celebrated on the pitch with a shirtless Lallana, but there is much work to do if the Reds are to advance to the
Capital One Cup final at the expense of Stoke, visitors to Anfield for the semi-final second leg on Tuesday night.
It had looked like new signing Steven Naismith would be an instant hero for the Canaries after Dieumerci Mbokani cancelled out Roberto Firmino's opener with a brilliant back-heel.
Naismith scored his first Everton goal against Liverpool and, on his debut following his move from Goodison Park, the Scot struck again to give the Canaries a 2-1 half-time lead.
Poor defending allowed Norwich to further extend their advantage when Alberto Moreno felled Naismith in the box and Wes Hoolahan converted the resulting penalty.
Jordan Henderson reduced the deficit from a gaping hole in the Norwich defence and another appeared allowing Firmino to equalise with 27 minutes remaining.
James Milner converted for 4-3 after capitalising on Russell Martin's dreadful pass back before the late drama.