The Belgium star produced one brilliant turn to leave Daniel Ayala trailing in his wake only to delay just long enough for the defender and his centre-back partner Ben Gibson to get back and snuff out the threat.
Of all the midfielders on show, however, Idrissa Gana Gueye caught the eye, the Goodison new boy is already looking a snip at £7.1m from Aston Villa on his work-rate alone.
Barry, meanwhile, was going about his business in the same manner he had done in 599 previous Premier League matches – mopping up in midfield, keeping it simple and generally being solid.
That was until Ashley Williams got in the way of Valdes at a corner and Barry instantly lashed home an angled shot to make it 1-1 in the 22nd minute.
If Middlesbrough argued Williams had impeded their goalkeeper, Everton thought they had cause for complaint about the visitors’ opener three minutes earlier.
Negredo appeared to head Stekelenburg’s hands and not the ball, forcing the goalkeeper to divert Stewart Downing’s cross into his own net.
A furious Stekelenburg, who left himself open to some criticism by not being physically stronger under pressure, was booked for his protests.