Lafferty was however fortunate to still be on the pitch as he had complained to boss Steve Cotterill that he was suffering from a blister.
The home side started brightly and nearly went in front following a mistake by former Burnley goalkeeper Marlon Beresford, who spilled a shot from Lafferty but managed to block the follow-up attempt by Andy Gray.
From Burnley's first corner of the game Alan Mahon's delivery from the left found the head of central defender Michael Duff, but his effort was straight at the Luton goalkeeper.
A free-kick from Mahon again found the head of Duff but his effort was blocked by Leon Barnett, with Steve Howard also blocking the rebound from Chris McCann.
Warren Feeney wasted the visitors' best opportunity when firing wide from the edge of the box.
It was still something of a surprise when Luton took the lead three minutes before the break with a fine move involving skipper Kevin Nicholls and fellow midfielder Ahmet Brkovic and it was striker Rowan Vine who shot beyond Brian Jensen.
The home side looked for a quick reply, but Beresford was equal to Mahon's 25-yard free-kick and McCann shot wide from the edge of the box.
The Clarets continued to press forward at the start of the second half with a surging run and pass by Mahon finding Lafferty, only for Beresford to block his shot at the expense of a corner.
Luton's Dean Morgan went close to extending the visitors' lead and was unfortunate to see his delicate lob beat Jensen, only to land on top of the crossbar.
At the other end Lafferty was again denied by a combination of keeper Beresford and captain Nicholls, who cleared off the line as far as Gray, but his shot was saved by the Luton goalie.
Beresford produced another fine save as a cross from Graham Branch found the head of James O'Connor, as the Luton goalkeeper leapt to his left to maintain the Hatters' lead.
Burnley finally got the equaliser their play merited when substitute Garreth O'Connor combined with James O'Connor to find Lafferty, and the 19-year-old fired past Beresford for his first senior goal for the Clarets.