Ian Harty struck a hat-trick as Annan beat Peterhead in the Ramsdens Cup at Galabank.
Harty's close-range effort opened the scoring and Muirhead struck with a 20-yard free-kick 11 minutes later.
He added a third on 46 minutes before James Redman responded with a 20-yard effort that nestled into the bottom corner.
Rory McAllister fired in from the spot for Peterhead, but Harty's late header from close range sealed the win.
Annan Athletic: Mitchell, Muirhead, Gibson, Neilson, McGowan, Bell (Sloan 86), Steele, Gilfillan, Cox (McKechnie 87), Harty, O'Connor (Peter Watson 90). Subs Not Used: Summersgill, Jardine.
Goals: Harty 20, Muirhead 31, Harty 48, 87.
Peterhead: Duffy, Davidson, MacDonald, McBain, Donald, Sharp (Bavidge 46), Watson, Redman, Conway, McAllister, Beasley. Subs Not Used: Salmon, Wyness, David Ross, Young.
Booked: Duffy, McBain, Redman, MacDonald, Donald. Goals: Redman 49, McAllister 75 pen.
Ref: Stephen Finnie