Arfield put Burnley ahead with a right-footed finish in the 18th minute before Vokes made it 2-0 three minutes before the interval.
Matt Smith scored a header 11 minutes from time to give Leeds hope, but Burnley held on to go second in the Championship.
They were deserving of a first success at Elland Road since 2004 too, having been far superior until the hour mark and then defending well when Leeds converted their industry into something resembling danger.
United's manager Brian McDermott has spoken often of his want for a winger, but it was poor defending and errant finishing which cost them in this one, with Luke Varney and Ross McCormack both culpable of the latter.
Other chances would come and go, but Burnley rode them out and gained the reward for a brilliant first-half which started with them rattling in three early shots to set the tone.
Arfield and Dean Marney both worked Paddy Kenny from the edge of the area, before the experienced goalkeeper produced a brilliant one-handed save to deny former Leeds loanee Vokes from six yards.
Leeds did momentarily threaten as Varney headed over but all signs had pointed to Burnley scoring first and that was what they did with 18 minutes gone.
Kieran Trippier's cross found Arfield at the back post and, even though Sam Byram - back after a lengthy hip injury - blocked his first shot, he remained alert enough to beat Kenny at his near post on the rebound.
Leeds have been desperately short of goals this season as they try to fashion a side in the absence of a genuine target man, but another chance did go their way with 21 minutes gone, Varney again squandering by drilling at Tom Heaton from six yards.
Despite their lack of punch Leeds continued to look for ways in, but Burnley remained the sharper, crisper side and deservedly went 2-0 up in the 42nd minute.
The goal carried heavy shades of the opener as Vokes got to Michael Kightly's cross and although Kenny dealt with his header, he was unopposed as the rebound sat up nicely for him. Leeds contested a free-kick in the build-up but two episodes of bad marking could not be ignored.
Leeds felt further angst as they headed to the dressing rooms, claiming Aidy White had been fouled in the box, but referee Lee Probert showed no interest.
The interval did little to halt Burnley's momentum and only errant finishing from Vokes stopped them scoring a goal from a move which started in their own box, before a recovering Rudy Austin just about deflected a Danny Ings cracker over the bar.
Kenny had to bail Leeds out again shortly after as he pushed away another Ings shot, while at the other end a wayward header from Ross McCormack was not what the home side needed.
Even when they did get a sight of the goal Heaton brilliantly pushed away an El-Hadji Diouf header, while he also frustrated Dom Poleon just after the striker had been booked for a match-ending challenge on David Jones.
A route-one approach would get Leeds on the scoresheet, though, with towering striker Smith on hand to head in a Diouf free-kick with 10 minutes left.
Austin and Poleon tried to complete a comeback after that but Leeds were left disappointed.