Alex Ferguson gave the Bluebirds a great start at Hardenhuish Park by opening the scoring after just eight minutes. However, they were unable to add to that and just past the hour-mark, Reece Hales equalised from the penalty spot.
Redditch are now in eighth place while Merthyr Town and Banbury United are fifth and sixth respectively after both secured wins on Tuesday night.
The Martyrs beat mid-table Kettering Town 2-0 at Penydarren Park, thanks to Ian Traylor after 22 minutes and a second to eventually make sure from Josh Yorwerth a minute into stoppage time at the end of the game.
Banbury won 4-1 at fourth-bottom St Neots Town to move up to sixth.
However, they had to come back from being a 12th minute Rogan McGeorge goal down to win, thanks to Eddie Odhiambo after 36 minutes, Jack Self right on the stroke of half-time and a George Jeacock brace in the 75th and 85th minutes.
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