Rangers deservedly claimed the most significant victory yet of their return to top flight football to ease the scrutiny on manager Mark Warburton and deepen the woes of his Aberdeen counterpart Derek McInnes.
For Rangers, it was a desperately-needed outcome in the wake of their 2-0 defeat at Hearts on Wednesday night as they reclaimed second place in the Premiership table.
Warburton responded to the midweek defeat at Tynecastle by making five changes to his starting line-up and also tweaking his 4-3-3 formation, deploying Miller in a deeper role than normal.
With Joe Garner making his presence felt as the focal point of the attack and support from the flanks being provided by Michael O’Halloran and Barrie McKay, the hosts shaded a forgettable first half without finding a cutting edge.
Garner was first to threaten when, after a smart exchange of passes with McKay, his eighth-minute shot was deflected just wide.
Aberdeen’s responded with James Maddison and Graeme Shinnie combining to find space on the left and the full-back’s cross deserved better than the tame connection from Jayden Stockley.
Rangers could not be accused of the passivity which had marked so much of their work against Hearts three days earlier, although early bookings for Hodson and Rob Kiernan suggested they needed to temper their approach.
READ MORE: Ross County 2 - 2 Hearts: Jamie Walker misses late penalty
They should have opened the scoring in the 24th minute when Aberdeen were carved wide open at the back as Lee Wallace raced clear onto a piercing pass from McKay. The Rangers captain had the goal at his mercy, but dragged his shot wide.
A timely intervention from Considine then denied Garner as the hosts tried to seize the initiative.
Both teams were being handicapped by a lack of composure in the attacking third of the pitch, as evidenced by Aberdeen captain Jack, whose unconvincing shot from a promising position was deflected wide seven minutes before the interval.
It was, at least, more positive from the visitors, who started the second half with greater intent. They passed up a glorious opportunity to go ahead three minutes after the resumption when Jonny Hayes cross from the left found Stockley unmarked on the edge of the six-yard box, only for the big striker to skew his header wide.
Aberdeen were left to rue his profligacy when Miller gave Rangers the advantage just four minutes later. Hodson took a free-kick quickly, catching Aberdeen flat-footed. Garner whipped over a cross from the right, the ball finding its way to the back post and Miller drove it beyond Joe Lewis from close range.
The momentum was now firmly with Rangers, although O’Halloran almost surrendered it with an injudicious backpass which set Maddison free on goal. But, in keeping with his out-of-sorts display, the midfielder scuffed his shot straight at Wes Foderingham.
O’Halloran was replaced by Martyn Waghorn and the substitute, out of favour in recent weeks, made a quick impact with his involvement in Rangers’ second goal in the 71st minute. It was a slick move, involving him, Hodson and McKay on the edge of the penalty area, but the Aberdeen defence were pulled apart far too easily and Hodson took full advantage by smashing home.
That effectively settled matters before stoppage time produced a flurry of cards and Aberdeen’s consolation goal. Hill was first to depart, earning his second caution as he had his first, for a foul on Maddison.
As the officials struggled to control proceedings, Jack picked up his second yellow card for an off the ball clash with Waghorn, just before Considine headed home a Maddison free-kick in the final act of the afternoon.