The visitors completely outplayed Dunfermline during a first half in which Higdon and Jamie Murphy, via a deflection, both netted and Chris Humphrey added a third shortly after the break.
The Pars finally made a game of it in the final quarter with Joe Cardle claiming a double - both of them deflected - but Higdon grabbed another in the last minute.
Dundee United produced an incredible late comeback to snatch a dramatic 3-3 draw in a thrilling Tayside derby at St Johnstone.
The visitors took a first-minute lead through Barry Douglas and continued to dominate the opening exchanges, but Francisco Sandaza's controversial penalty brought Saints back into the match in the 34th minute and Liam Craig's drive and then a second from Sandaza gave the hosts two-goal half-time advantage.
The Perth men looked comfortable but United ensured a stirring climax with two goals in four minutes to rescue a point. Substitute Gary Mackay-Steven gave the Tangerines hope in the 79th minute and then defender Gavin Gunning salvaged a point for his side with a header seven minutes from time.
Graeme Shinnie's late winner earned Inverness a 2-1 win over Kilmarnock and lifted Caley Thistle off the bottom of the table.
The full-back's low strike with two minutes to go secured a 2-1 win at the Tulloch Caledonian Stadium - Inverness' first victory of the campaign.
The hosts took the lead in the 25th minute when Gregory Tade powered home a close-range header before Dean Shiels levelled with a 25-yard curler nine minutes later.