McDonald headed the Dons into the lead after 61 minutes at Pittodrie with only his second touch after replacing the injured Andrew Considine.
The Dons then doubled their advantage four minutes later with a Miller penalty after Paul Quinn had been sent off for a last-man challenge on Darren Mackie.
Aberdeen striker Mackie returned after missing last week’s defeat by Rangers at Ibrox with a hamstring injury, while Mark McGhee handed Slovakian international Maros Klimpl a first start for Motherwell.
Graeme Smith was the busier of the two goalkeepers in the early stages of a scrappy game on a cold day at Pittodrie.
The Well keeper first pulled off a superb save to thwart Mackie from six yards, although the Dons striker was adjudged to be offside in any case, before punching a Charlie Mulgrew free-kick away to safety.
At the other end, Keith Lasley stung the palms of Jamie Langfield with a powerful drive from the edge of the box before a Bob Malcolm free-kick was easily saved by the Aberdeen custodian after 25 minutes.
The game finally burst into life after 30 minutes when a neat flick from Miller put Mackie in on goal but the Dons striker wasted the opportunity by unsuccessfully trying to square the ball for Sone Aluko when he should have shot himself.
The home supporters were then appealing for a penalty when both Lee Mair and Mackie fell in the box under pressure from Chris Porter and Klimpl as they tried to connect with an inviting Mulgrew corner but referee Chris Boyle waved play on.
As the half drew to a close Mulgrew brought the best out of Smith with a dipping free-kick from 25 yards.
However, it was Motherwell who should have taken an undeserved lead into the break but Jamie Murphy blasted the ball over the bar from 15 yards.
The second half continued in the same scrappy style of the first, although Motherwell enjoyed slightly more of the ball. Porter was causing a nuisance of himself in the Dons box and Considine did well to head clear with the tall striker lurking.
Calderwood was forced to make his first change of the day when Considine injured himself blocking a Porter effort.
McDonald came on for the young defender with Scott Severin dropping back into the Dons’ back four. The change had an immediate impact with McDonald heading an Aluko cross into the Motherwell net with only his second touch of the game.
Calderwood brought on Jeffrey de Visscher for Derek Young soon after as the Dons looked for a second. And the home fans did not have to wait long for their side to double their lead.
De Visscher crossed for Mackie, who looked certain to score before being bundled over in the box by Quinn. Referee Boyle had no choice but to send Quinn off and Miller stepped up to lash the ball past Smith from 12 yards for his fourth goal of the season.
Steven Saunders, who had replaced Murphy after 67 minutes, made a great last-ditch tackle to deny Mackie as the Dons looked for a third against 10-man Well.
Mair somehow failed to get a third for the Dons as his effort came back off the post and Chris Maguire, who had replaced the tiring Aluko, could not convert the rebound.
Malcolm and Maguire were both booked as the game became increasingly dirty and Mark Reynolds joined them in the referee’s notebook soon after.
Severin almost grabbed the goal of the day with a fierce drive from distance that took a deflection off Mackie but Smith made an impressive save.
Mulgrew and De Visscher both shot wide before referee Boyle blew for full-time, giving the Dons their second win of the season over McGhee’s side.