The Red Devils moved five points clear of their bitter rivals ahead of their trip to Anfield next weekend after goals from Marouane Fellaini, Michael Carrick and Wayne Rooney sealed a comfortable win.
Brendan Rodgers’ Liverpool side make the short trip to Swansea City on Monday night looking to reduce fourth-placed United’s lead to two points.
Former Reds centre-half Carragher felt Louis van Gaal’s side produced one of their best performances of the season against Spurs at Old Trafford.
Carragher wrote on Kicca: “One of Man United’s best performances just before they come to Anfield has put Liverpool under pressure tomorrow at Swansea.
“If Liverpool could win it will enable them to have it in their own hands for a top-four place but won’t be easy against the Swans.”
United have just won two of their last seven games away from home in the Premier League ahead of their trip to Anfield.
The Red Devils lost 1-0 on Merseyside last season after Daniel Sturridge scored a fourth-minute winner in September 2013.
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