Clint Marcelle and Nicky Eaden had wasted two glorious chances inside the opening six minutes and the home side were further denied by a couple of fine saves from the impressive West Bromwich Albion goalkeeper, Alan Miller.
But Redfearn pounced in the 34th minute. John Hendrie's shot was blocked by Miller but Redfearn followed up to score from close range.
The home side increased their lead five minutes before the break when a rash challenge from Paul Agnew sent Marcel crashing to the turf.
Referee Terry Heilbron immediately pointed to the spot and wing-back Neil Thompson converted the penalty.
Barnsley: Watson, Eaden, Appleby, Sheridan, Moses, De Zeeuw, Hendrie, Redfearn, Wilkinson (Liddell, 45), Marcelle (Bullock 72), Thompson. Substitute not used: Bosancic.
West Bromwich Albion: Miller, Murphy, Agnew (Coldicott, 45), Sneekes, Mardon, Raven (Butler, 80), Donovan (Taylor, 61), Smith, Peschisolido, Hunt, Hamilton.
Referee: T Heilbron (Newton Aycliffe).Reuse content