Negredo had a goal ruled out five minutes from time
Sunderland are rock-bottom in the Premier League and Middlesbrough are only a place above them and both look increasingly doomed.
This was a game Boro needed to win, but they were left cursing referee Martin Atkinson, who ruled out an effort from substitute Alvaro Negredo five minutes from time after refusing to send off Burnley defender Michael Keane moments earlier.
Former Clarets loan striker Patrick Bamford, a late sub for Boro, was brought down by last man Keane as he headed for goal but the England centre-back was only booked.
Stewart Downing¹s edge-of-area free-kick was deflected wide and when the ball came to Negredo following the resultant corner, he turned and fired in with Burnley midfielder Joey Barton flat out in the box.
But the end result means Boro have now gone 14 league games without victory, while Burnley are still searching for their first away win in any competition this season.
Boro caretaker boss Steve Agnew abandoned the bold 4-4-2 system that came unstuck in the 4-2 defeat at relegation rivals Hull on Wednesday and made four changes in switching to a back three.
Martin Atkinson was at the thick of it this afternoon
Among the casualties in the shake-up was leading scorer Negredo, who dropped to the bench despite hitting the opener at the KCOM Stadium.
Cristhian Stuani started instead in another courageous move, but Boro failed to pose a serious threat before Burnley struck the woodwork on 13 minutes.
Daniel Ayala looked to be harshly penalised for climbing on the back of Ashley Barnes on the edge of the box.
And from the free-kick, Robbie Brady¹s curler clipped the bar with keeper Victor Valdes at full stretch.
Burnley right-back Matthew Lowton, who this week extended his contract to 2020, found George Boyd in space in the 26th minute.
Get Quotes on Home Insurance
But after bringing the ball under control neatly, Boyd scorer of the only goal in Tuesday¹s home win over Stoke showed a lack of composure with his finish as he blazed over.
Premier League relegation odds 2016/17
Mon, March 6, 2017
Which Premier League side is favourite to go down this season?
1 of 12
Stoke – 275/1
Boro struggled to make any real impression in the first half and, when Antonio Barragan whipped a ball in from the right, Rudy Gestede¹s glancing header was well wide.
The home side saw another chance escape them when skipper Grant Leadbitter¹s free-kick was flicked on and Stuani couldn¹t get on the end of Ayala¹s ball in from the left.
There was a flashpoint shortly before the break when Burnley left-back Stephen Ward was guilty of a violent shove on Barragan as the visitors were about to take a corner.
Inevitably, Barton was in the thick of the melee that followed. Atkinson awarded Boro a free-kick and, after a confusing delay, eventually got round to booking Ward.
Burnley keeper Tom Heaton was finally called on to make a save early in the second half when he fell to his right to hold Gestede¹s header.
It was enough for Agnew to rethink his plans but, while he prepared Negredo to come on for Stuani, Burnley almost took the lead after a delightful move.
Middlesbrough are still six points away from safety
Ward broke down the left and pulled the ball back for Barnes, whose dummy opened up an opportunity for Brady, but the Republic of Ireland winger fired wide.
Heaton earned his pay on 68 minutes with a magnificent one-handed stop from Negredo, who met Downing¹s left-wing cross with a spectacular bicycle kick.
Adama Traore then replaced Gestede as Agnew sought to inject more energy into his attack.
But when Traore¹s potent mix of trickery and pace set up a chance for Adam Clayton, the midfielder produced a tame shot that was easy for Heaton.
Burnley had penalty claims waved away on 74 minutes when Ward centred from the left and sub Sam Vokes¹ effort struck Bernardo.
Brady bent a free-kick over the defensive wall, but it didn¹t dip sufficiently to test Valdes. Boro then went for broke with Bamford¹s introduction in a lively but fruitless finale.
MIDDLESBROUGH: Valdes 7; Ayala 6, Bernardo 5 (Bamford 83rd), Gibson 6; Barragan 6, Clayton 5, Leadbitter 6, Forshaw 5, Downing 6; Gestede 6 (Traore (69th) 6), Stuani 5 (Negredo (58th) 6)
BURNLEY: Heaton 7; Lowton 6, Keane 6, Mee 6, Ward 7; Boyd 6, Barton 5, Hendrick 6, Brady 8; Barnes 6 (Tarkowski 90th); Gray 5 (Vokes (62nd) 5)