In doing so, for the first time in the Premiership for 15 weeks, they suggested that the most worrying of all the ailments which have afflicted them may not yet prove terminal.
Two second-half goals conjured by Juninho left Everton on the suffering end of Middlesbrough's first victory in 13 league games. Their last dated back to 14 September: a 2-1 success at Goodison.
It was, moreover, only their sixth since Boxing Day last year, when a win at Everton would have elevated them to the dizzy heights of second place. "Games against Everton always seem to be turning points for us," Robson said. "I hope this will be another one."
That much remains to be seen. As Robson was quick to point out, the defensive deficiencies which have undermined Middlesbrough's ambitions of upward mobility threatened to trip them up again yesterday.
It was his good fortune that the collective spirit, and the skill of Juninho, was a potent enough blend to overcome any self-inflicted damage and an Everton team weakened by the absence of Andrei Kanchelskis with 'flu, as well as Andy Hinchcliffe.
Dave Watson's enforced withdrawal, with a suspected rib fracture, came as another blow to Joe Royle. The Everton manager was without his trusty on-field lieutenant from the 15th minute and was not a happy man as he prepared to depart from Teesside.
"Quite honestly, I can't believe what I've seen," Royle said. "I don't know why we didn't get a penalty when Nick Barmby was brought down in the first half and their third and fourth goals came from what should have been awarded as fouls."
There may have been a hint of sour grapes but it remained a mystery to everyone save Steve Dunn why Everton were not awarded a penalty when Gary Walsh hauled down Graham Stuart, let alone when Barmby's legs appeared to be taken from under him by Emerson.
It might have been different, too, had Gary Speed's second-minute volley crept inside Walsh's left-hand post instead of clipping it and deflecting wide.
As it was, Middlesbrough grasped their opportunity to set a revivalist performance in motion. Stuart cleared a Fabrizio Ravanelli header off the line after 20 minutes and two minutes later Craig Hignett fired Boro ahead.
It was a neat side-footed finish but the opening came courtesy of Emerson - "Yes, he's here" the man on the Tannoy proclaimed when reading out the teams - whose nonchalantly flicked pass with the outside of his right foot, highlighted the talents he can bring to the Middlesbrough team when he's in the area (England that is; not the penalty area).
Having done the hard part Boro reverted to banana-skin mode. Derek Whyte pawed at Speed's cross and David Unsworth duly administered punishment from the penalty spot.
Clayton Blackmore, playing his first game for Middlesbrough since February, beat Neville Southall with a curling 25-yard shot in the 37th minute yet Boro could still not hold on to the lead until half-time. Duncan Ferguson rose unchallenged to head-in Barmby's right-wing cross in stoppage time.
Middlesbrough showed the greater resolve thereafter. They showed more creative spark, too - or, rather, Juninho did. The Everton defence could not find a way to stop the elusive little man from Sao Paulo. On four occassions Juninho cut in from the right; on two of them he scored.
First, in the 57th minute, he beat Southall at the second attempt. Then, with 16 minutes left, he slid in his second after playing a wall-pass with Ravanelli.
Middlesbrough (4-4-1-1): Walsh; Liddle, Cox, Vickers, Whyte (Morris, h-t); Hignett, Blackmore, Emerson, Beck; Juninho; Ravanelli. Substitutes not used: Fjortoft, Freestone, Summerbell, Roberts (gk).
Everton (3-4-1-2): Southall; Barrett, Watson (Allen, 15; Hottiger, 71), Unsworth; Stuart, Grant, Parkinson, Speed; Barmby; Branch (Rideout, 67), Ferguson. Substitutes not used: Limpar, Gerrard (gk).
Referee: S Dunn (Bristol).