After Scott Arfield opened the scoring for the Clarets, Vokes, who also netted twice at QPR earlier this month, followed up with two goals in 10 minutes as the hosts went into the break well in charge.
Djamel Abdoun hit back for the visitors towards the end, tapping in after seeing his penalty saved - but Forest could not prevent the hosts easing eight points ahead of them.
Burnley started brightly and almost opened the scoring in the first five minutes when Arfield broke into the box but his shot was hacked off the line by Jamaal Lascelles.
They got the breakthrough their enterprising opening had deserved on 12 minutes as Arfield nutmegged Danny Fox on the edge of the box and lashed past Karl Darlow in the Forest goal for his fifth league goal of the season.
The Clarets continued to threaten, as Michael Kightly evaded the challenge of Gonzalo Jara in midfield before rifling an effort harmlessly wide.
Sean Dyche's side doubled their advantage in the 22nd minute when Kieran Trippier fired a wonderful cross to the back post and Vokes headed the ball beyond the helpless Darlow.
Forest's unbeaten run in the Championship, which stretched back to late November, looked in serious jeopardy as Vokes forced Darlow into a magnificent save before a Michael Duff header was ruled out for offside.
It got worse for the away side 10 minutes before the break as Vokes added his second of the game when his deflected effort looped past Darlow, prompting a wave of disgruntled cries from the Forest fans at the break.
The visitors looked rejuvenated after half-time and Rafik Djebbour tested Tom Heaton for the first time with a header from inside the box.
A corner from Abdoun then found its way to Lascelles, whose effort came back off the crossbar when the defender looked certain to score.
Forest continued to pile on the pressure in search of a way back into the game and Lascelles once again went close - but this time his header was cleared off the line by substitute Keith Treacy.
Danny Ings had a glorious chance to increase Burnley's lead in the second half as he thundered an effort over the bar after a sublime lay-off from Vokes inside the area.
Forest were given a lifeline as a sublime interchange between substitute Simon Cox and Jamie Paterson saw Cox brought down in the box for a penalty.
Heaton did superbly to keep out Abdoun's spot -kick but the stopper was helpless as the Algerian pounced on the rebound to grab a consolation for Forest.