Adam Rooney and Niall McGinn gave the visitors a 2-0 lead before Groningen pulled one back just before half-time. But the contest arguably turned on a brilliant save by Jamie Langfield just after the hour.
Michael de Leeuw, one of two Groningen forwards sent on at half-time to try to turn round the deficit, found himself in space 12 yards out and seemed certain to score, but Langfield thrust out a right boot to steer the shot away as it went past him.
Derek McInnes set up his team with a five-man defence to try to counter the attacking threat of Danny Hoesen and the flying Serb, Filip Kostic, while Groningen named an unchanged side from the goalless first leg.
The match was preceded by an impeccably observed minute's silence for the 298 victims of the Ukrainian plane disaster last Thursday, which has devastated the Netherlands.
In a lively opening 10 minutes, Groningen had the first real chance when defender Johan Kappelhoff looped a header from a corner beyond the reach of Jamie Langfield, only to see Jonny Hayes clear off the line.
A mistake by right-back Eric Botteghin then put Adam Rooney through on the left, but the goalkeeper Sergio Padt was out quickly to smother the danger.
Groningen had a glorious chance to go ahead as Tjaronn Chery put Kostic through on the left-hand flank, but the Serb was unable to capitalise, dragging his shot wide of Langfield's left-hand post.
The Dutch side looked comfortable in possession, but their long punts rarely tested Aberdeen's well-organised defence.
After 15 minutes Flood picked up a loose ball and carried it to the corner of the penalty area, where Hayes made room for for a shot that stung Padt's gloves.
That seemed to give Aberdeen the confidence to break forward more, with Flood and the outstanding Hayes taking turns to ask questions of Groningen down their right-hand side.
Then, the visitors went ahead on 24 minutes through Rooney's penalty. Hayes took advantage of Groningen's malfunctioning offside trap to collect a punt from midfield and charge into the area before going down nder the challenge of Eric Botteghin. The contact looked marginal, but replays showed the right-back had left his foot trailing.
Despite protests from the Dutch players, referee Daniel Stefanski immediately pointed to the spot and Rooney took full advantage, driving the ball low to Padt's right.
Seven minutes later they doubled their lead with a goal that left the Groningen players fuming, but owed much to defensive indiscipline. Andrew Considine's looping header found Rooney in space, and the striker smartly lobbed the ball over Padt and against the crossbar.
It rebounded to an unmarked Niall McGinn, who crashed it in beyond the helpless goalkeeper, but the Dutch were convinced that Rooney had been offside. The Dutch pushed forward, with Chery trying his luck with a rasping drive from 25 yards that Langfield was relieved to see go wide.
The vistors' defence stood firm until two minutes from time, when Lindgren's looping ball from the right-hand channel found the head of Maikal Kieftenbeld. The midfielder's downward header was just too powerful for Langfield, who was unable to claw it away before it crossed the line at his right-hand post.
With Groningen needing to score twice in the second half, it was no surprise to see Erwin van de Looi bring on two strikers after the break, as De Leeuw and Jarchinio Antonia replaced Hoesen and Kieftenbeld. De Leeuw immediately looked lively on the left, flashing a shot across Langfield's goal within three minutes. There was a bigger scare for Aberdeen when Cherry went down on 57 minutes as Flood appeared to hold back the striker, but the referee waved away the Dutch protestations.
Groningen then looked certain to score on 62 minutes when a long crossfield pass landed at the feet of Nick van der Velden, who found De Leeuw unmarked on the penalty spot, but Langfield's superb stop denied him.
Peter Pawlett, who had posed the main threat for the visitors in the first leg, was replaced on 66 minutes by Barry Robson as Aberdeen looked to shore up the midfield.
Mark Reynolds then nearly put the ball into his own net as Kostic found space and fired in a dangerous cross from the left, but managed to steer it just wide of the post.
Minutes later the referee waved away fresh Groningen calls for a penalty as De Leeuw claimed to have been pushed on the edge of the area.
The goalkeeper was equal to Groningen's increasingly hair-trigger shooting, blocking one speculative effort from Botteghin with his chest and getting down smartly to stop Cherry's drive creeping inside his right-hand post.
Aberdeen could have doubled their winning margin five minutes from time when Ryan Jack's shot was deflected just beyond the post. By then, though, the spark had gone out of Groningen's challenge and Aberdeen were able to hold on comfortably.