In front of a crowd of 442, Ben Adelsbury was given his marching orders in the 73rd minute for two yellow cards and Shane White followed him in the 84th minute after receiving a straight red.
Taunton, who began the game with a twelve-point lead at the top, took only 6 minutes to open their account with Dan Sullivan slotting home.
Sullivan became provider in the 15th minute when he set up Les Afful who made it 2-0.
Cirencester pulled a goal back in the 20th minute when Ben Whitehead scored.
Taunton appeared to be heading for victory when they ran into trouble when first Adelsbury was ordered off followed by White.
However, they hung on to gain another three points.
Bristol Manor Farm remain in second spot after a 1-0 home win over mid-table North Leigh.
Kye Holly`s goal 8 minutes before the break proved decisive for the league new boys, who will be delighted with the first half of their first season at this level.
Salisbury FC are third, a point behind Manor Farm with a game in hand, after beating third-bottom Mangotsfield United 3-0 at the Raymond McEnhill Stadium.
A good pre-Christmas crowd of 650 saw Owen Howe maintain his good scoring form since signing for the Whites by converting a 17th minute penalty after he had been brought down in the box.
Claudio Herbert doubled the hosts` advantage 9 minutes later and then Stuart Green ensured the points stayed at home with a third on the hour-mark.
Swindon Supermarine, AFC Totton and Wimborne Town complete the play-off picture, with Winchester City level on points with the latter in seventh, and all won on Saturday, apart from Totton, whose game at Barnstaple Town was postponed due to a waterlogged pitch.
Supermarine were comfortable 4-0 winners at the WebbsWood against Cinderford Town.
Aaron Woodley gave `Marine a 15th minute lead, but they had to wait until the hour-mark before Josh Parsons doubled that with his 100th goal for the club.
Bradley Gray, back after a spell with Evesham United, added a third on 73 minutes and that was quickly followed by a second for Parsons.
Wimborne hammered bottom-markers Bishops Cleeve 7-1 on the Mitres` oen patch.
Jack Lovell gave the Magpies an early 4th minute lead that an own goal by Ben Tunnicliff doubled 3 minutes later.
And the game was all-but over by the 13th minute as Wimborne had scored two more through Toby Holmes and Lovell again.
Jack Watts notched a consolation for the Mitres 4 minuets later, and then second half goals from Louis Kellaway, Matt Oldring and Lee Francis took the score to 7-1.
Winchester were only marginally lighter on fifth-bottom Shortwood United, running out 5-1 home winners.
It was scoreless until the 38th minute when Jamie Barron gave City the lead and 6 minutes later, Pat Cox made it 2-0.
Joe White pulled one back 10 minutes after the break, only for Ollie Bailey to make it 3-1 on 76 minutes and then Cox went on to complete his hat-trick on 78 and 89 minutes.
Fourth-bottom Slimbridge made it a bad day for the teams at the wrong end of the table as they were beaten 4-1 at home by a Paulton Rovers side who are now sixteenth.
Goals from new signing Jack Ball after 13 minutes and Dale Evans 9 minutes later gave Rovers a cushion.
Evans added a third on 69 minutes, with Michael Bryant reducing the arrears shortly afterwards, only for Ball to add his second a minute from time.
Elsewhere, Yate Town continued their climb up the table with a 3-1 home win over Kidlington, thanks to Ben Brooks after 38 minutes, Nick Peare on 67 minuets and a Lewis Leigh-Gilchrist penalty 20 minutes from the end – all after Duran Martin had given the visitors a 28th minute lead from the spot.
Evesham United won 2-0 at home to Larkhall Athletic, courtesy of Matt Liddiard`s spot-kick breaking the deadlock just shy of the hour-mark, followed by a Lewis Powell effort on 71 minutes, while there were no goals at the Loop Meadow where Didcot Town and Bideford shared a 0-0 draw.
By Steve Whitney
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