With the game seemingly heading for a stalemate as a resolute Palace stood their ground at Selhurst Park it was up to the Danish star to find the net from range and secure a 1-0 win.
The victory means that Spurs are four points behind London rivals Chelsea with five games left to play.
Elsewhere, there were narrow wins for both Arsenal and Middlesbrough.
The Gunners needed a late winner to keep their top-four hopes alive as they beat Leicester 1-0 at the Emirates Stadium to move up to sixth place.
Arsene Wenger's side were denied by the woodwork towards the end of the first half when Alexis Sanchez struck the crossbar, but they eventually scored at the death as Nacho Monreal's shot deflected in off Robert Huth.
At the Riverside an early strike by Martin de Roon was enough for Boro as they beat fellow relegation strugglers Sunderland 1-0.
De Roon gave the hosts an early lead when he scored in the eighth minute after neatly controlling and finishing a cross from Adam Clayton.
The visitors offered very little going forward as Boro hung on to secure all three points.