Debutant Hogan Ephraim broke the Bristol City duck in the first half with a clever finish before Malaury Martin equalised for the hosts with a powerful effort in Saturday's clash at the Riverside.
Ryan McGivern was sent off late on for City but Middlesbrough failed to test Dean Gerken, starting in place of David James, as much as they would have liked.
City's first away point of the year will serve them well in their battle against relegation, while promotion hopefuls Boro will be left frustrated at failed to press home their numerical advantage.
The visitors flew out of the traps as Jon Stead teed up Stephen Pearson, but the Scot could not manoeuvre the ball onto his left foot quickly enough to get a shot away.
City took the lead in the 13th minute. Pearson played in Ephraim, who got away from Matthew Bates before delicately clipping the ball over the onrushing Steele to give him a debut goal and City their first away breakthrough in eight attempts.
Boro's response was restricted to long-range efforts, with Lukas Jutkiewicz's turn and shot flying just over the bar.
City who had the last clear-cut chance of the half, after Neil Kilkenny worked his way to the byline before teeing up Pearson, whose shot flew high over Steele's goal.
Indeed, the home side's failure to test Gerken at all saw the side booed off at half-time, with City deserving their lead at the break.
City remained on top in the second half, with Stead charging forward before shooting just over.
But out of nothing, Middlesbrough equalised as Martin, who scored a stunning late winner at Ashton Gate earlier in the season, let fly from just outside the box with a powerful strike past Gerken.
The hosts suddenly had the bit between their teeth and Gerken had to use his head to prevent a Joe Bennett cross from drifting in.
Merouane Zemmama's shot then flew just past the post, before Gerken saved City after Bart Ogbeche had got on the end of an Adam Hammill cross.
Life was made more difficult for City as McGivern bundled down Jutkiewicz with the striker bearing down on goal. McGivern was deemed the last man and was dismissed by referee Colin Webster.
However, despite the numerical advantage Boro failed to test Gerken again and despite a frantic finish, neither side could find a winner.