Ajax's advantage had been cut to one point after Twente's 2-0 win over Vitesse on Saturday, but Schone's treble ensured that Frank de Boer's men continued to set the pace on Sunday.
Schone completely overshadowed the Eredivisie top scorer Alfred Finnbogason, with Heerenveen failing to register a single shot on target during the game.
The Denmark international scored twice from the penalty spot in the opening 18 minutes before completing his hat-trick eight minutes from time as Ajax extended their unbeaten league run to 12 matches.
Feyenoord, meanwhile, lost ground on the top two after being held 1-1 at mid-table NAC Breda.
Daryl Janmaat put Feyenoord in front in the 25th minute, but Rydell Poepon's penalty hauled the sides level 12 minutes later.
The hosts saw substitute Stipe Perica sent off in the 84th minute for serious foul play just two minutes after he was introduced, but Feyenoord could not force a winner in the closing stages.
At the wrong end of table, Cambuur climbed out of the bottom three with a 3-1 home win over PEC Zwolle.
Marcel Ritzmaier put Cambuur ahead in the ninth minute before Martijn Barto scored either side of half-time to put the result beyond doubt, Steve Fernandes Pereira netting a consolation for Zwolle 12 minutes from time.
Elsewhere, Tjaronn Chery's third-minute goal was enough to earn Groningen a 1-0 win over Go Ahead Eagles.
