Right from the start Lynn had that extra yard of pace, having had the benefit of a midweek fixture after the lay-off while Grantham were playing their first match since December 12.
Grantham managed, throughout the match, just one header which went wide, a couple of corners and a scrambled goal disallowed for a clear offside.
They were backpedalling and the likes of ex-Notts County players Brindley and Stubbs were under heavy pressure in defence. Cox on the Grantham goal made vital first half saves to keep out shots from Burrows and Watts.
In the 57th minute Grantham won their first corner which came to nothing, and almost immediately were hit by two quick goals.
Paul Chapman got the first in the 62nd minute with a far post header after winger Burrows had pulled the Grantham defence apart.
Three minutes later Cox pulled down Chapman when he was breaking clear and the penalty was tucked away by Clive Adams.
The only way Grantham could escape fro defeat was if the fog caused the game to be abandoned and Lynn must have been thankful that the conditions did not deteriorate.
In the 85th minute Chapman forced his way past Stubbs and hammered in an angled shot which Cox found too hot and the ball slipped through the keeper's fingers and over the line.
Lynn: Drewery, Wilson, Bircumshaw, Johnston, M Wiles, Watts, Thompson, Adams, Burrows, Biggins (sub D Wiles 85), Chapman.
Grantham: Cox, Thacker, Jarvis, Brindley, Stubbs, Foster, Jones (sub Tandy 70 mins), Nixon, Young, Leadbetter, Hines.
Referee: M Claridge (Rotherham) Attendance: 400