Smith lit up a tight contest with a superb 25-yard strike two minutes into the second half and soon ran beyond a static defence to make it two.
The Danes folded and an own goal by Mikael Antonsson and Richard Foster’s strike rounded off a memorable night at a sold-out Pittodrie as the Dons secured European football beyond Christmas for the first time in more than 20 years.
Calderwood said: “It really was (magnificent), a great performance from the lads. We know they are capable of it which is why we get so angry on Saturdays – but it was a wonderful night.”
Calderwood also admitted being in the draw gave the club reason to look ahead.
He continued: “It’s wonderful, something to look forward to, but all credit to the lads.
“It doesn’t matter who you get now, it gives you something to look forward to in February.”
Elsewhere Everton claimed a 3-2 UEFA Cup win at AZ Alkmaar.
The visitors twice let a lead slip, Andy Johnson scoring after just 64 seconds, only for Graziano Pelle to level.
Phil Jagielka made it 2-1 to Everton but Kew Jaliens equalised again before James Vaughan finally settled it.
The result saw AZ crash out after Nurnberg came from behind to win 3-1 at Larissa to climb from fourth to second place.
The Toffees became the first side to beat AZ on home turf in Europe and jubilant manager David Moyes paid tribute to his troops afterwards.
“They all performed really well against a good side,’’ he said.
“I think we’re getting stronger as we go along.
He added: “Tonight we tried to give as many of our players as possible a game.
“We need them fit for the Christmas period and ready.’’
Elsewhere Substitute Simao Sabrosa netted a stoppage-time free-kick as 10-man Atletico Madrid secured top spot in the group with a last-gasp 2-1 win against Panathinaikos, who dropped to second.
Dimitrios Salpigidis put the Greeks ahead but former Liverpool player Luis Garcia equalised for the Spaniards, who went on to win despite a straight red card for Raul Garcia.
Jozef Kozlej put the home side ahead but goals from Ivan Saenko, Marek Mintal and Angelos Charisteas completed the turnaround.
Fiorentina and AEK Athens both secured qualification from Group C after the former beat Mlada Boleslav 2-1.
A penalty from former Chelsea striker Adrian Mutu gave the Italians the lead.
Jan Rajnoch levelled, but substitute Christian Vieri sealed the points.
AEK progress despite losing 2-1 at home to Villarreal, who sealed top spot in the group.
Antonio Mavuba put the visitors ahead, Rivaldo equalised, but former Newcastle striker Jon Dahl Tomasson restored the lead a minute later.
Group D saw Rennes and Dinamo Zagreb play out a 1-1 draw that saw both sides eliminated.
A victory for either might have seen one of them qualify but Stephane M’bia Etoundi’s 88th-minute equaliser denied Dinamo, who led through Ognjen Vukojevic.
Former Liverpool midfielder Bruno Cheyrou also missed a penalty for the home side.
Hamburg finished top of the group after a 1-1 draw against second-placed Basle, who ended the game with 10 men.
Ivan Ergic put the visitors ahead after team-mate Reto Zanni was sent off.
Ivica Olic levelled for the Germans.