Victory stretched Liversedge’s recent unbeaten run to five matches and Jonathan Rimmington’s men end January having taken eight points from four games since the turn of the year.
It also heaped further misery on the Miners, who slipped to an eighth straight league defeat and remain perilously close to the relegation zone.
Although Liversedge dominated the physical battle, Rainworth held their own for an hour, until the visitors took control to seal a 15th win of the season which allowed them to move up to sixth place.
Liversedge dominated the early stages and almost took a seventh minute lead when a Rainworth attack broke down and the visitors countered quickly but Gibril Bojang’s effort was saved by Ben Townsend.
Stephen Wales shot wide after beating two defenders before Walton went in on goal but his effort was also off target.
Rainworth went close when Thomas Poole shot over from a good position but Liversedge were quick on the counter attack and Vaughan Redford shot over following another break.
Rainworth created three chances of their own but were unable to convert, while Wales shot just over the moments before half-time.
Liversedge broke the deadlock two minutes after the re-start when Walton rose above the defence to powerfully head home a cross.
Rainworth grabbed a 57th minute equaliser when Matt Harris found Nick Langford and he slotted past goalkeeper Sam Andrews.
Liversedge responded in style and Walton raced in on goal and was tripped by Jack Weatherall.
Wales stepped up and gave Townsend no chance with the penalty to regain the lead.
Wales beat two defenders but his shot came to nothing when a pass to two unmarked players in the area may have been the better option.
Liversedge secured all three points when Walton rose to head home a free-kick in the 85th minute.