Taulava's effort, midway through the second half, was the difference between the two sides and had Gordon Ross not missed with three kickable penalties, Welsh could have easily come away with the points.
The visitors edged the forward battle and had more possession and territory but lacked the creativity to break down a stubborn home defence as they failed to capitalise on the yellow-carding of Taulava.
Worcester began poorly; Chris Pennell spilled the ball in the first tackle for the Warriors to be penalised allowing the Welsh a line-out in the home 22. Welsh produced a fierce drive and Worcester again offended to allow Ross to kick a simple penalty.
That was soon nullified by a penalty from Andy Goode, after Welsh were offside in midfield, before Ross had a chance to restore the advantage but his 45-metre kick fell short.
Welsh had the better of the first 15 minutes, with their strong scrum and powerful runs from Jonathan Mills and Ed Jackson allowing them to dominate in terms of territory and possession.
However, a poor pass from Ross placed his side under pressure, giving the Warriors a platform in the visitors' 22. Nikki Walker was held up in the in-goal area as Welsh kept their line intact but conceded a second penalty to Goode, as the Warriors took a 6-3 lead after 22 minutes.
The first half was a desperate affair with only flickering signs of any attacking invention.
There was a neat kick over the defence by Goode for Josh Matavesi to collect and an enterprising touchline run from David Lemi, in which he beat two defenders, but little else to enthuse the crowd.
Just before half-time, Worcester suffered a double blow when firstly Taulava was sin-binned for offside at a maul and then Ross fired over the resulting penalty to tie up the scores at the interval.
Taulava returned with no further damage to the score line but still it was Welsh who had the better of the opening exchanges of the second half. Ross kicked skilfully to keep the visitors going forward as Worcester had considerable difficulty in breaking out of their own half.
A poor pass from Matavesi resulted in the Warriors being penalised but Ross missed the penalty chance and it proved costly as suddenly from nowhere Worcester produced a stunning try.
From inside his own 22, Matavesi started the move with an elusive run, Goode made the next inroads before Alex Grove carved open the Welsh defence with a clean break. The ball was recycled for Matavesi to make ground before sending Taulava over for the try which Goode converted - giving the Warriors a 13-6 lead going into the final quarter.
Worcester nearly scored again when neat footwork from Lemi saw him race away and kick ahead but Dan Caprice got back to beat the Warriors' wing to the touchdown.
Four minutes from time, Ross had another penalty chance but his kick was badly mishit and sailed wide for Worcester to cling on for a fortunate victory.
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