Nelsen and fellow-last minute deadline day signing Louis Saha were both among the seven substitutes for the high-profile fixture in which Spurs defended stubbornly to deny the hosts victory.
Spurs stayed third and moved on to 50 points, seven behind leaders Manchester City and five adrift of champions Manchester United.
Liverpool remained seventh after welcoming back Uruguayan striker Luis Suarez, who came on as a 66th-minute substitute following a nine-match absence which included an eight-game ban for racially abusing Manchester United defender Patrice Evra.
Andy Carroll had Liverpool's best chance but skied a half-volley over the bar after 74 minutes and Spurs winger Gareth Bale fired straight at Pepe Reina after 85 minutes with only the Liverpool keeper to beat.
Spurs manager Harry Redknapp, who hoped to be at the match after the end of court proceedings in his tax evasion trial in London, was unable to get to Liverpool as his plane developed a technical fault and could not fly.
There were few chances at either end and one of the highlights of the first half was when a cat ran on to the pitch and caused a short delay.
