Morecambe slipped into the League Two relegation zone with defeat at fellow strugglers Forest Green Rovers.
The Shrimps were beaten 2-0.
Barrow began life under Ady Pennock with a much-needed 3-1 home win over Aldershot Town in the National League.
Adi Yussuf scored a hat-trick.
Lancaster City progressed in the FA Trophy with a 1-0 win at Mossley; Kendal Town are out after a 4-2 home defeat by Atherton Collieries.