The visitors belied their lowly NPL Premier Division position with a gritty display, but two goals in a three minute spell in the first half secured Jono Greening's side another victory, to take them to fourth in the table, writes Steve Adamson.
The Boro line-up showed three changes from the midweek draw at league leaders Matlock Town, with Will Thornton, Kieran Weledji and Simon Heslop replaced by Dylan Cogill, Ryan Watson and Luca Colville.
Visitors Grantham included full-back James Williamson, who made eight appearances for Boro in 2019, and it was Grantham, attacking the Shed who made the brighter start, creating a couple of good openings in the first 10 minutes.
A Lee Shaw cross was headed goalwards by Joe Wafula, but Bailey Gooda deflected the effort wide, then Wafula connected with a through-ball from Williamson, but skied his shot over the bar.
Boro's first goal attempt came on 14 minutes when Cameron Wilson shot narrowly over, then Jake Day fired wide of the left hand post, and a surging run from Kieran Glynn led to him passing to Colville, who laid off to Wilson, and his snap-shot was deflected wide by a defender.
Boro opened the scoring on 26 minutes, when Ash Jackson launched a long throw into the penalty area, and Day rose above the keeper to guide his header into the net.
Just three minutes later the lead was doubled, when a Colville cross was headed home by Brad Plant at the far post.
Boro could have added to their tally, as Wilson laid off to Watson, who shot into the side-netting, then Day flicked on for Plant to fire straight at the keeper.
Grantham then created a couple of chances just before the interval, with Shane Clarke blazing a shot over, and a cross from Shaw was headed off the Boro goal-line by Gooda.
The second half was evenly fought, with few clear chances created, although Colville struck a thunderous 35-yard shot that flashed over the bar.
The closest either side came to scoring was on 69 minutes, when sub James Cadman, who had only been on the pitch four minutes, raced forward and fired in a powerful shot, but keeper James Pollard dived to save.
Cadman then set up a chance for Kieran Glynn to drill a shot just past the post.
Late on, both skipper Elliott Durrell and Ricky Miller shot over for Grantham, as Boro comfortably held on for the three points, and a third successive clean sheet.
Not a vintage Boro performance, but good displays throughout the team, with a special mention for Cogill, who replaced the suspended Thornton, and had a terrific game, winning numerous headers and tackles.
Plant was another to shine, but Colville, whose movement and passing was superb all game, claimed the man of match award.
BORO: Whitley, Watson, Jackson, Colville, Cogill, Gooda, Plant (Cadman 65), Maloney, Day, Glynn, Wilson (Hutton 83)
MAN OF MATCH: Luca Colville