The Lions dominated the early part of the game but Boro had the best chances with Kris Boyd having a shot blocked and goalkeeper David Forde tipping over Gary O'Neil's deflected effort.
The away side took the lead on the quarter hour as Liam Trotter crossed for Puncheon, signed on loan from Southampton on Tuesday, to convert from inside the box.
Middlesbrough searched in vain for a second-half equaliser but Leroy Lita missed with two headers meaning Boro slipped into the drop zone.
Source: PA
Source: PA