The home team started well with skipper Steven Caldwell having a header from a Robbie Blake corner cleared off the line by Diego Leon.
At the other end Burnley failed to clear a Brian Howard free kick and left-back Lewin Nyatanga curled a shot just wide of the post.
Burnley did have the ball in the net after 19 minutes from the head of Caldwell but this was disallowed by referee Webster for a foul.
A through ball by Leon on 24 minutes sent Daniel Nardiello racing clear, but with only Brian Jensen to beat, he shot wide of the target.
Burnley took the lead with Barnsley reduced to ten men as central defender Dennis Souza left the field to receive treatment, Elliott took full advantage to beat Luke Steele after being played in by a lovely Robbie Blake pass.
With Souza still absent Burnley struck again on 36 minutes with Lafferty, who scored twice for Northern Ireland in midweek, taking a short pass from Jon Harley and curling a beauty beyond Steele.
With half-time approaching Barnsley pulled a goal back as Nardiello eased past Graham Alexander and found Leon and while his close-range effort was blocked by Jensen, the rebound fell calmly for skipper Howard to convert.
Blake went close ten minutes into the second half, but Steele saved his strike at the second time of asking, while James O'Connor volleyed wide after the Tykes defence had failed to clear a Blake free-kick.
The home team created a further opportunity on 66 minutes with a fine move involving Joey Gudjonsson, Lafferty, Blake and finishing with Elliott shooting wide from the edge of the box.
Barnsley almost grabbed an equaliser when Jon Macken's shot from 20 yards beat Jensen but clipped the top of the crossbar.
Not to be outdone Gudjonsson drove a shot from fully 25 yards against a post with Steele well beaten.
Barnsley substitute Michael Coulson had an opportunity to score late on, but headed wide a cross from full-back Rob Kozluk.