The visitors may have turned over Swiss side Grasshoppers on Thursday night, but three days later it was Steve McClaren's men who were well and truly rolled over.
For after Sheringham had netted with his first touch, assistant referee Bone then signalled for a second goal when the ball had clearly had not crossed the line.
Just one spot had separated these two sides at the kick-off and despite making four changes, it was 11th-placed Boro, buoyed by that UEFA Cup victory in Zurich, who started the most confidently.
Indeed, after Gaizka Mendieta left his wayward 20-yard free-kick nestling in the TV gantry, the recalled duo of Fabio Rochemback and Massimo Maccarone each went close towards launching McClaren's side into the top half of the table.
West Ham, in tenth place, had made two changes from the side that lost 2-1 at Manchester City last weekend and while keeper Shaka Hislop - deputising for the injured Roy Carroll - had been kept on full alert early on, striker Bobby Zamora then began to stimulate the Eastenders' response.
Having replaced the rested Sheringham, the Hammers striker burst clear before wastefully sidefooting to Mark Schwarzer and when he raced away again a few minutes later, he was cynically upended by the consequently booked Doriva on the edge of the Boro penalty area.
The visitors' cause was not helped by the loss of Gareth Southgate with a groin injury midway through the half and his replacement Franck Queudrue soon found the lively Yossi Benayoun a handful too.
After the Israeli twice went close, Hayden Mullins also sent a sizzling volley inches wide, before Mendieta's curling 20-yarder almost broke the deadlock as the interval neared.
Just after the restart Yakubu forced Hislop into a low save and, on the hour, Boro tried to turn up the heat by bringing on Jimmy Floyd Hasselbaink for the ineffective Maccarone.
But after Benayoun saw his tightly-angled shot cleared off the line by Queudrue, Pardew replied by pitching on Sheringham.
It was to prove an inspired switch, for within seconds of his 65th minute arrival, the Hammers' substitute was in the right place at the right time to sweep home Paul Konchesky's low, left-wing centre from eight yards out.
And after having their veteran striker to thank for putting them on the way to a hard-fought victory, West Ham were even more grateful to ageing referee's assistant Bone when he incorrectly signalled that Schwarzer had clawed the ball back from behind his goal-line after Konchesky's free-kick into the box took a deflection off the hapless Chris Riggott.
Boro were understandably furious that they had become the latest victims to a lack of video technology that would have confirmed Mr Bone's decision had left them out on a limb and, leading the protests, George Boeteng was booked by referee Steve Bennett for dissent.
And although Queudrue rose highest at the near post to glance home Rochemback's late, late corner, it was far too late to prevent Boro from going down to defeat.