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Adebayo Akinfenwa scored his seventh goal of the season to hand Gillingham a fifth successive League 2 victory on Saturday.
A diving header from the striker seven minutes from half-time was enough to separate the sides in a closely-fought encounter at Priestfield.
And the three points were enough to lift the Gills into the play-off places for the first time this season.
There were few goal opportunities for either of the teams in the opening 45 minutes of the first-ever competitive meeting between these two sides.
The best early chance for the Gills came 16 minutes in when Cody McDonald raced onto a ball from Akinfenwa, but keeper Chris Day saved with his feet.
Stevenage were reliant on some heavy-handed play and hitting the Gills on the break. It was an impressive passing move, however, that led to a good chance from the visitors when Byron Harrison’s close-range header was saved one-handed by Alan Julian.
Nerves were calmed when on 38 minutes Danny Spiller whipped in an inviting cross and Akinfenwa headed home. The big striker ended the half with a shot which keeper Day needed to get behind.
A quiet start to the second half soon livened up when McDonald had a flurry of chances.
A series of defensive blocks and saves from Day denied the striker as he had five chances in a seven minute spell.
The Gills almost paid dearly for those misses and had Julian to thank for saving what seemed like a certain goal, as he blocked Rob Sinclair’s 84 minute shot. Joe Martin did equally well to slide in and block the follow-up.
Hearts were in mouths during the resulting corner as a free-for-all ended with a Gillingham free-kick,
Four nervy injury-time minutes were played at the end of 90 minutes and Gillingham hung on.
Gills: Julian, Fuller, Nutter (Barcham 67mins), Lawrence, Gowling, Weston, Maher (Bentley 76mins), Spiller, Martin, Akinfenwa (S Payne 76mins), McDonald. Subs not used: King, Rooney, Jackman, Cronin.
Stevenage: Day, Wilson, Laird, Foster, Long (Sinclair 60mins), Griffin, Roberts, Beardsley, Mousinho, O’Shea (May 72mins), Harrison (Odubade 62mins). Subs not used: Bayes, Byrom, Winn, Maamria.
Gillingham striker Adebayo Akinfenwa celebrates his winner against Stevenage Picture: Barry Goodwin