Nathaniel Clyne gave the ball away for the Clarets’ first goal, with Gray finding Vokes to blast home.
Steven Defour, on his Burnley debut, was allowed to charge forward and set up Gray to roll home the second.
Liverpool had 81% of possession and 26 shots – but only tested Clarets keeper Tom Heaton with efforts from distance.
The 19% of possession that the Clarets had is the lowest total by a winning side in the Premier League since Opta began recording the statistic in the 2003-04 season.
Burnley only had one other effort at goal, which was off target, but the figures belied how little threat the Reds posed when they came forward.
Liverpool were a shadow of the attacking force they were in last week’s thrilling 4-3 win at Arsenal and their second away game of the season ended in their first defeat of the new campaign.
The game had been switched to Turf Moor because work on the new stand at Anfield is not complete and, after losing to Swansea in their opener, Burnley made home advantage count this time to pick up their first points since their promotion.
The Reds had problems at the other end too. Philippe Coutinho starred as Liverpool’s forward play gave them victory last week – but he was a long way short of his best on this occasion.
Time and time again the Brazilian picked up the ball in space on the edge of the Burnley area looking to bend in one of his trademark spectacular goals but, of his nine strikes from similar range, only one brought a save from Tom Heaton.
The manner of their victory at Emirates Stadium had given Liverpool plenty of reasons for early season optimism but, unfortunately for them, the only part of that performance they repeated came at the back.
Left-back Alberto Moreno paid the price for his defensive errors at the Emirates, being replaced by James Milner, but right-back Clyne produced an even worse error that led to Burnley’s opener.
Ragnar Klavan also should have done better when he failed to stop Defour’s run forward, leaving Liverpool’s defence wide open for Gray to make it 2-0.