Allan Russell had quickly atoned for his penalty miss against Ayr by firing Kilmarnock into an early lead.
But sublime finishes either side of half-time from Miller lifted the Dons above Hearts in the race for a European spot.
Kilmarnock were on their way to moving into the top six until Miller's first goal laid the foundations for their sixth defeat in seven home matches.
Killie started well although Sone Aluko, playing up front in Aberdeen's 3-4-3 formation, gave an indication of the open first half to come when he shot narrowly wide from 20 yards.
Russell had failed to give his side a two-goal lead during their 2-2 derby cup draw, but his luck turned in the 10th minute.
Scott Severin was harshly penalised by referee Eddie Smith as he beat David Fernandez in the air 25 yards out. The free-kick was rolled short to Garry Hay, whose fierce but wayward strike rebounded off team-mate Danny Invincibile and fell kindly for Russell to blast home from eight yards.
Russell had another good chance when he met Willie Gibson's corner at the near post, but he could not direct the header on target.
Aberdeen survived another scare when Zander Diamond deflected Craig Bryson's first-time effort over the crossbar after Invincibile had cut the ball back.
Killie were well on top but they were given a warning when Gary McDonald headed inches wide from Charlie Mulgrew's deep cross.
And the Dons levelled in the 29th minute when Miller flicked Mulgrew's near-post corner past Damien Rascle with his heel.
Bryson had a great opportunity when he timed his run to perfection to meet Gibson's low cross, but Jamie Langfield blocked from close range.
Chances were now falling at both ends and Rascle, in for the suspended Alan Combe, spilled Mulgrew's 30-yard free-kick but cleared with his foot.
Andrew Considine then cleared Russell's header off the line following Hay's enterprising run, and the Kilmarnock left-back soon blocked twice from Darren Mackie inside his own box.
Despite being posed problems on the break by Russell's strong running, Aberdeen took control after the break.
Rascle beat away Miller's powerful 25-yard free-kick before the Dons striker grabbed his 10th goal of the season in the 59th minute.
Aluko laid the ball off to Mackie on the right flank, and Miller stooped to meet his cross and guide his header over Rascle and into the far corner.
Aberdeen soon had chances to kill off their hosts. Mulgrew slipped the ball through a gaping hole in the home defence and Aluko side-stepped Rascle and Frazer Wright but could not thread his finish past Pascali on the line.
Moments later the Italian defender was shrugged off by Miller following a high ball by Mulgrew, but Rascle got down well to save the Aberdeen goalscorer's 20-yard drive.
Aberdeen's back three thwarted Russell in the six-yard box as he tried to guide home Hay's inviting cross, but Killie otherwise struggled to find the killer pass despite increasing pressure. Mehdi Taouil completed his return from a hamstring injury when he was brought on amid much expectation, but he was booked moments later for reacting angrily to Mackie's foul as Miller lay injured.
Mackie, Diamond and Fernandez were also cautioned for their part in the ensuing melee as the yellow card count rose to seven.
The visitors sat deep but Kilmarnock's last serious chance went begging in the 87th minute when Gibson volleyed Taouil's cross into the ground and inches beyond the far post.