ON-LOAN striker Danny Bloomfield showed just why Norwich City hold him in high regard as Lynn - semi-finalists for the past two years - made smooth progress into the hat for the second round.
Bloomfield (19) scored the opening goal and displayed flashes of his ability before his 68-minute Linnets debut came to a premature end after picking up a knock on his knee.
Linnets manager Tony Spearing said: "Danny did well considering he hadn't played with any of the lads before tonight.
"I knew what he was about and thought he got in some great positions. He took his goal very well."
A delighted Spearing, who rested Zeke Rowe, Kevin White and Roger Joseph for the tie, added: "We deserved that result. It was our reward for how we've played in the last few weeks.
"We've just beaten a side that hadn't lost for seven or eight games, and who I believe will gain promotion, and we cruised it.
"The lads played very much within themselves after the break but we were 'always comfortable out there."
After a dour opening 20 minutes, Lynn finally managed to take control, with Jamie Clarke and Bloomfield in particular a menace to the home defence.
In the 22nd minute the 19year-old showed his first glimpse of class with a sharp turn before he was hauled to the ground having left the Grantham player in his wake.
Five minutes later he turned Grantham inside out again but slipped at the crucial moment on the edge of the box.
In the 30th minute Wayne Anderson headed over from five yards out as the Grantham goal began to live a charmed life.
The opening goal arrived four minutes later when a quick throw from Jason Minett found Clarke, who unselfishly turned the ball into the path of Bloomfield to score.
In the 38th minute Louis Evans and Anderson were involved in a neat exchange of passes before Evans fired the second home.
Lynn tried their best to hand Grantham, who fielded former Linnets Dave Taylor and Wayne Hallcro, a lifeline just seconds after the restart.
Simon Dakin's back-pass left Steve Wilson in deep trouble, with the Lynn keeper hitting his clearance straight into the path of Stuart Wilson.
The Grantham forward had the goal at his mercy, but his sidefoot shot trickled towards the line for Wilson to scramble back and gratefully clutch on.
In the 60th minute Clarke was denied by the legs of keeper Riccardi, and 16 minutes from time Anderson planted another header over the bar from five yards out when it would have been easier to steer it in the net.
Grantham left Lynn with an anxious few minutes when the referee and his assistant deemed that Brendan McDaid's volley had crossed the line after coming back off the underside of Wilson's woodwork.
Grantham: Riccardi, George, Shaw, McDaid, Hallcro, Wilkins, Howley, Foster, Taylor, Wilson, Hall. Subs not used: Bull, Dye, Ranshaw.
Lynn: Wilson, Dakin, March, Evans, Fuff, Clark, Minett, Hayes (Hudson 72), Bloomfield (Jones 68), Clarke, Anderson. Not used: Wright.
Attendance: 248. MoM: Craig Clark. Referee: Mr J. Murfitt (Ely).
Bookings, Grantham: Shaw (51, late challenge).