The success put the Clarets second, with Middlesbrough not in action and Brighton thrashed 4-1 by Cardiff City.
Vokes gave them the lead from the spot in the first half after debutant Lloyd Doyley brought down George Boyd.
Rotherham frustrated the hosts for much of the game but Arfield ended lingering fightback hopes with a late second.
Joe Newell had the Millers' best chance in a rare raid forward, but failed to beat goalkeeper Tom Heaton from close range.
Sean Dyche's side dominated but did not fully capitalise on the chances that came their way, with Andre Gray's header brushing the crossbar and goalkeeper Lee Camp making good saves from Boyd and Stephen Ward to keep the score down.
Burnley are now unbeaten in nine Championship games, but the size of Warnock's task in dragging Rotherham out of danger was evident as they mustered just one shot on target at Turf Moor.
The defeat left the visitors third from bottom and five points adrift of MK Dons, the team immediately above them.
Burnley manager Sean Dyche:
"It was hard work. Neil (Warnock) being Neil has got a new group and has got a bit of fervour to them. They came here, I imagine, with no expectation and tried to play on that.
"They broke the game up and it was a disjointed game. But as ever, I like the fact we can win games in different ways.
"We have won it outrightly with the chances with have made, we have deserved victory."
Rotherham manager Neil Warnock:
"I am really happy, they can't be too down.
"You don't play Burnley every week. We have got some tough games but teams that we will play against will have some tough games.
"We are looking forward to the challenge."
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Match ends, Burnley 2, Rotherham United 0.
Second Half ends, Burnley 2, Rotherham United 0.
Sam Vokes (Burnley) wins a free kick in the attacking half.
Foul by Greg Halford (Rotherham United).
Attempt missed. Sam Vokes (Burnley) header from the centre of the box is too high. Assisted by Stephen Ward with a cross.
Substitution, Burnley. Matthew Taylor replaces George Boyd.
Substitution, Burnley. Rouwen Hennings replaces Andre Gray.
Stephen Ward (Burnley) wins a free kick in the defensive half.
Foul by Jonson Clarke-Harris (Rotherham United).
Goal!  Burnley 2, Rotherham United 0. Scott Arfield (Burnley) right footed shot from the centre of the box to the high centre of the goal. Assisted by Andre Gray.
Richard Smallwood (Rotherham United) is shown the yellow card for a bad foul.
Scott Arfield (Burnley) wins a free kick in the defensive half.
Foul by Richard Smallwood (Rotherham United).
Attempt missed. Richard Smallwood (Rotherham United) left footed shot from outside the box misses to the left.
Foul by George Boyd (Burnley).
Jonson Clarke-Harris (Rotherham United) wins a free kick on the right wing.
Attempt blocked. Scott Arfield (Burnley) right footed shot from the centre of the box is blocked. Assisted by Stephen Ward with a cross.
Attempt blocked. Sam Vokes (Burnley) right footed shot from the centre of the box is blocked.
Attempt saved. George Boyd (Burnley) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Andre Gray with a cross.
Attempt missed. Joe Newell (Rotherham United) right footed shot from the centre of the box is close, but misses to the right. Assisted by Jonson Clarke-Harris.
Attempt saved. Andre Gray (Burnley) right footed shot from outside the box is saved in the centre of the goal. Assisted by Matthew Lowton.
Offside, Burnley. Scott Arfield tries a through ball, but Andre Gray is caught offside.
Substitution, Rotherham United. Leon Best replaces Lloyd Doyley.
Attempt saved. Kirk Broadfoot (Rotherham United) header from the centre of the box is saved in the top centre of the goal. Assisted by Greg Halford.
Ben Mee (Burnley) is shown the yellow card for a bad foul.
Foul by Ben Mee (Burnley).
Jonson Clarke-Harris (Rotherham United) wins a free kick in the attacking half.
Offside, Burnley. Matthew Lowton tries a through ball, but Andre Gray is caught offside.
Andre Gray (Burnley) is shown the yellow card.
Foul by Andre Gray (Burnley).
Lloyd Doyley (Rotherham United) wins a free kick in the defensive half.
Attempt missed. Joe Newell (Rotherham United) right footed shot from long range on the right misses to the left. Assisted by Andrew Shinnie.
Offside, Rotherham United. Kirk Broadfoot tries a through ball, but Jonson Clarke-Harris is caught offside.
Foul by Scott Arfield (Burnley).
Andrew Shinnie (Rotherham United) wins a free kick in the attacking half.
Joey Barton (Burnley) wins a free kick in the defensive half.
Foul by Richard Smallwood (Rotherham United).
Corner,  Rotherham United. Conceded by James Tarkowski.
Foul by David Jones (Burnley).
Jonson Clarke-Harris (Rotherham United) wins a free kick in the attacking half.
Goals from Sam Vokes and Scott Arfield sealed a Championship victory for Burnley to extend Neil Warnock's wait for a first win as Rotherham boss.