Matip turned Pedro Porro's cross into his own net in the final minute of stoppage-time just when it looked as though Spurs had run out of ideas against a dogged Liverpool, who lost Curtis Jones to a straight red card in the first half and Diego Jota to two bookings with 20 minutes to play.
Heung-min Son bagged his sixth goal in four matches with a first-time finish from Richarlison's cutback ten minutes after Jones was dismissed for a studs-up challenge on Yves Bissouma.
Ten-man Liverpool hit back in first-half stoppage-time through Cody Gakpo's fierce drive and their task was made even harder after the break when half-time substitute Jota was dismissed after two fouls on Destiny Udogie.
Here's how we rated the Spurs players...
Guglielmo Vicario 7
Made a fine double save to deny Gakpo and Andy Robertson in the first half. Well beaten by the Dutchman's equaliser from close range.
Pedro Porro 9
Quietly excellent and deserved to be the man to fashion the breakthrough when Matip turned his cross past Alisson. Comfortable in possession, a threat in the final third and made a couple of last-ditch challenges to halt Liverpool counters.
Cristian Romero 7
Demonstrated his quality on the ball by pushing into midfield for most of the second half.
Micky van de Ven 6
Not tight to Gakpo for the equaliser and caught out a couple of times. His pace was important in covering behind in a stretched game, however.
Destiny Udogie 7
Dealt well with the threat of Mohamed Salah and twice drew yellow-card offences from Jota. Unfairly booked himself after winning the ball in a sliding challenge on Gakpo.
Pape Sarr 7
Still looks raw on the ball at times but his energy is important in end-to-end games. Made an important block to deny Robertson in the first half.
Yves Bissouma 8
His ability to get around the pitch was crucial against a Liverpool side who had to play on the break. Set the tempo against the nine men by keeping the ball moving quickly.
Dejan Kulusevski 6
Saw plenty of the ball and gave Robertson a tough evening but was too predictable at times and could not turn possession into many chances.
James Maddison 8
Unlocked Liverpool with a brilliant pre-assist for Son's goal in another decisive performance. Drew a magnificent save from Alisson in the second half.
Full of confidence on the left of the front three, linking up well with Udogie. Set up Son's goal with an unselfish pass and struck the post with a low effort.
Heung-min Son 8
Made his goal look easy again and close to a second, forcing Alisson into a great save and then having an effort ruled out for a Richarlison offside. Increasingly feels like an elite centre-forward rather than a winger.
Manor Solomon (Son 68') 6
Wriggled into a couple of shooting positions against a packed Liverpool defence.
Ben Davies (Udogie 83') 6
Solid in a late cameo.
Oliver Skipp (Sarr 83') 6
Did fine for the final 15 minutes.
Alejo Veliz (Maddison 90') N/A
A Premier League debut but not enough time to make an impact
Pierre-Emile Hojbjerg (Bissouma 90') 7
Made a difference with his willing running and quick use of the ball.
Not used: Forster, Skipp, Emerson, Davies, Phillips, Donley.