It may have ended in acrimony with a late altercation involving Middlesbrough’s Rudy Gestede and Manchester United’s Eric Bailly subsequently spilling over into the tunnel but, away from the sound and fury, both managers were left harbouring grounds for cautious optimism.

Hope can be a fragile commodity but on a day when goals from Marouane Fellaini, Jesse Lingard and Antonio Valenica lifted his side to fifth, José Mourinho can still dream of gate-crashing the top four while, thanks to Gestede, Boro at least scored their first goal in five League games.

They have now gone 11 games without a win but there were signs that life after Mourinho’s old friend Aitor Karanka, who was sacked on Thursday, might be looking up under the much more attacking interim manager Steve Agnew.

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With slow-motion replays indicating that initial suggestions Gestede had attempted to bite Bailly were inaccurate, Agnew should be free to deploy the 4-4-2 formation which enabled the 19th‑placed Boro to finish strongly here in their next three, vital games – against Swansea City, Hull City and Burnley.

Significantly, an afternoon which ended with Mourinho refusing to answer questions about his part in that tunnel fracas, neglecting to shake Agnew’s hand on the pitch and, not entirely convincingly, denying he had exchanged cross words with Stewart Downing, aka Karanka’s bete noire, left Boro’s caretaker quietly satisfied following an impressive second half.

Karanka’s successor might not have been left smiling had Marcus Rashford not spurned a highly inviting early opening, though. After meeting Lingard’s ball and proceeding to burn Bernardo off with that astonishing pace, the young striker – without a League goal since September – misplaced his shot, permitting Víctor Valdés to save.

Valdés’s own, unhappy, stint at United featured only a couple of first-team appearances but he showed off high‑calibre reflexes courtesy of a pair of quite stunning saves to first thwart Rashford’s attempt to turn in Juan Mata’s low cross and then, almost instantly, repel Valenica’s shot on the rebound.

Yet even Valdés was confounded when Ashley Young deceived the overstretched Antonio Barragan – experiencing an awful afternoon – before unleashing a deep cross met by Fellaini’s forehead. The Riverside emitted a collective groan as, played onside by Ben Gibson, Fellaini rose above Fabio before thumping a header beyond the goalkeeper’s reach. It was the Belgian’s first League goal since December 2015 and left Steve Gibson, Boro’s watching owner, looking rueful, as a tracksuited Agnew urged his troops to regroup.

If Valdés’s heroics were responsible for keeping Boro in the game and Rashford’s highly convincing Thierry Henry impression as, invariably cued up by Lingard, he persistently peeled away from the hapless, consistently outpaced Bernardo, was becoming an ominously recurring theme, there remained hints that a draw was not entirely out of the question.

While Downing, recalled to arms by Agnew after spending far too many months in Karanka’s deep freeze, showed off the odd classy manoeuvre, Gaston Ramírez, Álvaro Negredo and Marten de Roon all missed half chances while Negredo had a penalty claim against Phil Jones dismissed. Such skinny statistics failed to do justice to the clear improvement in Boro’s game. Infinitely more attack-minded than before, they enjoyed more possession than usual while Ramírez prompted persistent malfunctioning of the Bailly‑Valencia axis down United’s right.

Facebook Twitter Pinterest Marouane Fellaini heads Manchester United into the lead. Photograph: Lee Smith/Reuters

Unfortunately for Agnew, Lingard had clearly tired of playing in Rashford – who for all that exhilarating movement was repeatedly let down by his final ball – so when Mata set him free, he ignored a couple of decent passing options and simply accelerated to around 25 yards out, whereupon he dispatched a viciously bending shot which swerved away from Valdés as it curved, imperiously, towards the top corner. Once again, Bernardo and Barragan stood off.

Rather than opt for damage limitation, Boro’s caretaker aimed to at least end the goalless run by liberating Gestede and Adama Traoré from the bench. Evidently concerned by the former’s aerial ability and the latter’s pace, Mourinho displayed Karanka-esque pragmatism in replacing Mata with Marcos Rojo and switching from a back three to a back four.

Undeterred, Gestede, following Downing’s slightly speculative left‑wing cross, swiftly delighted in side-footing from close range Boro’s first goal in more than eight hours of League football. The ball was headed on by Negredo and then De Roon and, aided by botched attempts at clearing from Phil Jones and then Chris Smalling – the ball falling to the defender’s weaker left foot – Gestede revelled in applying the final touch.

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Under Karanka Boro rarely seemed to have sufficient bodies in the box to polish off such chances but their new‑found boldness indicated fortune really does favour the brave – not to mention ruffling Mourinho’s players, who were drawn into a spot of argy bargy as Boro pressed for an equaliser and Gestede and Bailly crossed swords.

In stoppage time a flattering gloss was applied to United’s victory as, attempting to make a routine clearance from Downing’s back pass, Valdés slipped, permitting Valencia to walk the ball into the net. No matter, Agnew was left with reason to believe survival remains within Boro’s grasp.