The Clarets won for the primary time because Sean Dyche's sacking way to Roberts' sublime curler and Nathan Collins' header.
Roberts' first aim for Burnley following his August move from Swansea came early in the first half at Turf Moor and proved the important thing moment.
It became simply their fifth league victory this term, in intervening time manager Mike Jackson's 2nd game since Dyche's surprise sacking closing week after 10 years in charge.
Third bottom Burnley stay in the relegation sector however they're now just one factor in the back of fourth backside Everton, who've a recreation in hand.
Burnley host Wolves on Sunday and, with Everton dealing with quadruple chasing Liverpool the identical day, Jackson's team are in with a threat of hiking out of the lowest three this weekend.
Just hours before kick-off, Dyche had spoken for the primary time considering his sacking, talking warmly approximately the "simply first-rate times" he enjoyed with Burnley.
There became a sense in some quarters that Burnley stagnated in the very last yr of Dyche's reign, but most effective avoiding relegation will again the membership's choice to sack him.
This became a small step within the proper path for Burnley and their chairman Alan Pace.
For the primary time considering 2012, Burnley were playing a domestic game without Dyche and they started nervously.
Southampton's Kyle Walker-Peters smashed a deflected strike that flashed simply huge for a nook.
