Chris Cohen
Billy Davies' side had to work hard for the three points that kept them in touch with promotion rivals Newcastle, who beat Preston.
But Cohen's goal, fired home in the 73rd minute, was enough to help the Reds eclipse the record set by Brian Clough's side in 1980.
That team won 12 matches on the bounce at the City Ground, but the run was divided over two seasons.
Forest went into half-time in frustrated mood, after failing to make the breakthrough against Middlesbrough.
Gordon Strachan's hard-working side, whose recent return to form had seen them push close to the play-off places, ensured chances were few and far between for the home side.
Raddy Majewski came agonisingly close for Forest, bending a 25-yard free-kick spectacularly against the bar.
The little Pole had previously bent an earlier effort into the side netting, as the home side struggled to find a breakthrough.
Forest were enjoying spells of pressure, but without managing to find a real gap in the Middlesbrough defence.
Robert Earnshaw could have netted the 151st goal of his career in the 28th minute, following a clever flick from Chris Cohen, but lifted his shot over the bar.
The visitors were finding chances hard to come by as well, despite winning a flurry of corners, with a weak Scott McDonald shot, struck on the turn from the edge of the box, the closest they came to scoring.
The second half saw Earnshaw threaten again with a shot on the turn that forced Coyne to get his body behind the ball at the near post, while Wes Morgan almost connected with a driven Majewski corner at the far post.
James Perch, as Majewski had been in the first half, was booked for a foul when he brought down Willo Flood in the centre circle.
Forest, generally, were again looking frustrated, with passes going astray, halting their stuttering momentum.
Cohen, after cutting onto his left foot on the right side of the box, bent a cross-cum-shot wide of the far post.
And, when Kelvin Wilson did fire the ball into the back of the net after the visiting defence had failed to deal with a Cohen corner, the defender's celebrations were cut short by an offside flag.
Forest finally managed to chisel a gap in the Middlesbrough armour as they produced a swift, flowing counter attack that carved the visitors open.
Majewski's touch gave him the chance to break down the left, before cutting into the centre for Dexter Blackstock. The striker, in turn, rolled the ball into the path of Cohen who produced a calm, composed finish, slotting the ball inside the keeper's near post from 12 yards.
It took a spectacular save from Camp, diving full-length to his left, to deny substitute Leroy Lita an immediate equaliser, as he struck a powerful shot from the edge of the box.
FOREST: Camp, Gunter, Morgan, Wilson, Perch, Anderson, Majewski, McKenna, Cohen, Blackstock, Earnshaw. Subs: Smith, Chambers, McGugan, Adebola, Garner, McGoldrick, Moussi.
BORO: Coyne, Naughton, Wheater, McManus, Pogatetz, Flood, O'Neil, Robson, Arca, Aliadiere, McDonald. Subs: Steele, Hoyte, Lita, Miller, Grounds, Franks, Taylor.
REFEREE: Phil Crossley, Kent