The Railwaymen started the day in the top six themselves and have always proved to be tough opponents for the Peacocks in the past.
But an impressive performance saw Taunton earn an early 7th minute lead through Dan Sullivan.
However, it wasn`t until the 65th minute that they managed a second through recent signing Matt Buse.
And then a Matt Wright brace on the 70th and 77th minute killed off the home side.
Bristol Manor Farm dropped down to fourth and were overtaken by Swindon Supermarine after Joe Selman`s 54th minute effort eventually proved enough for `Marine at the WebbsWood Stadium.
Salisbury FC are now second after they won 2-0 at lowly Barnstaple Town.
Goals from Stuart Green after 32 minutes and recent loan signing Zack Kotwica 6 minutes into the second half sealed the points for the Whites.
Bideford and Evesham United complete the top six, but neither managed a win on Saturday.
Bideford lost a seven-goal thriller at North Leigh.
Craig Duff gave the Devonians a 17th minute lead that George Seacole cancelled out in the 39th minute.
Parity lasted barely a minute though as Duff restored Biddy`s lead.
Matt Grabe levelled for the Oxfordshire side 9 minutes after the break and then Dejon Noel-Williams put them in front for the first time 4 minutes later and then a second for Seacole made it 4-2.
James Mayne made it an interesting late few seconds when he reduced the deficit to one in the 3rd minute of stoppage time.
Evesham had to make do with one point from a 1-1 home draw with an improving Yate Town side who have only lost one in their last six.
And they led through Ben Brooks` 32nd minute goal right until the 84th minute when Carl Brown salvaged a point for the Worcestershire hosts.
Bottom side Bishops Cleeve picked up only their fifth point of the season to date and four points from their last two games, after a 1-1 home draw with neighbours Slimbridge in a game of two spot-kicks – Elliot Kennedy converting for Cleeve in the 33rd minute and Adam Mace for the Swans 10 minutes from time.
Second-bottom Mangotsfield United also picked up a point after recording a third successive 1-1 draw, this time against Cirencester Town at Cossham Street.
Aidan Bennett gave the visitors an 18th minute lead that Kane Simpson eventually cancelled out with 10 minutes to go.
Larkhall Athletic won 2-1 at home to Paulton Rovers with goals from Joe Tumelty after 32 minutes and Matt Britton on 65 minutes – all after David Sims had given Rovers a 17th minute lead.
Wimborne Town were the day`s other winners, 5-2 at home to Shortwood United.
Jack Lovell and Toby Holmes both bagged braces for the Magpies, as did Sam Taylor in a losing cause, with Sam Bayston making it a nap hand for the hosts in stoppage time.
Seven goals at Wimborne, but none at Kidlington as they shared a goalless draw against AFC Totton.
Winchester City came from two-down to share the spoils at Cinderford Town in the day`s other game.
An Andy Lewis spot-kick after 23 minutes and Declan Morley-Lyne from open play a minute before the break had the Foresters in control.
Two-nil can often be a dangerous lead, and so it proved here as City fought back to level through Liam Gilbert after 61 minutes and Pat Cox 7 minutes from time.
By Steve Whitney
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