The Aberdeen defence, meanwhile, were able to limit their opponents to long-range efforts, which Jamie Langfield was also equal to.
Derek McInnes was able to field his normal starting XI with Jonny Hayes and Pawlett recovering from knocks sustained in the first round qualifying victory over Daugava Riga.
Groningen, who finished seventh in last season's Eredivise, named two new signings in their starting line-up, with former Ajax striker Danny Hoesen and goalkeeper Padt making their debuts
A cagey start to the first half saw both midfields cancel each other out, however it was the hosts that threatened first on 12 minutes.
After patient build-up play McGinn released Pawlett down the left and the midfielder saw his shot parried by Padt and then bounce off a defender for an Aberdeen corner that came to nothing.
With Willo Flood and Pawlett looking lively, Aberdeen continued to apply the pressure on their Dutch opponents with Padt being forced to come off his line quickly to deny McGinn and then did well to keep out a header from Hayes.
The home side had an appeal for a penalty waved away when captain Russell Anderson felt he was fouled in the box, with Portuguese referee Hugo Filipe unmoved.
With the first half looking to be fizzling out as quietly as it had begun, Groningen almost sneaked a crucial away goal just before the half-time whistle.
Full-back Hans Hateboar got the better of Hayes for pace down the right-hand side, his cutback was deflected off Mark Reynolds, but Langfield was on hand to save the defender's blushes. The loose ball then fell to Hoesen, who from a tight angle was unable to convert.
The second half started in similarly low-key fashion as the first, but began to get a bit heated with Pawlett and Hayes continuing to be the victim of unfair challenges.
Groningen saw two players cautioned as tempers began to flare, first Nick van der Velden saw yellow for a challenge on Hayes, while defender Johan Kappelhof picked up a booking for a foul on Ryan Jack.
On 62 minutes the visitors threatened again from long distance, this time midfielder Rasmus Lindgren found space on the edge of the box and he fired in a low shot that Langfield was forced to beat away behind for a Groningen corner.
Adam Rooney made way for Aberdeen's latest summer signing David Goodwillie, much to the delight of the 16,523 Pittodrie crowd, however the former Dundee United and Blackburn striker could not find that all-important goal for the Dons.
In the closing stages of the half it was Groningen once again who almost stole an away goal. The two substitutes Jarchinio Antonia and Dino Islamovic linked up well, with the later flashing a shot the wrong side of Langfield's near post.
It is not the worst result for Aberdeen, but they will now swap their usual surroundings of the north-east of Scotland for the north-east of the Netherlands, as they look to continue their European campaign.
Josh Law scored twice in the first 19 minutes of his Motherwell career, but Stuart McCall's men were pegged back by two penalties in a 2-2 draw against Icelandic side Stjarnan at Fir Park.
Law, who started just off John Sutton in his first appearance since a summer move from Conference side Alfreton Town, showed early promise in his bid to emulate brother Nicky's impressive two-year spell at Fir Park as he finished twice after getting ahead of the visiting defence.
Motherwell were well on top until the 35th minute when Olafur Karl Finsen converted a penalty after Keith Lasley was adjudged to have handled.
And they suffered a huge blow in injury-time when Finsen netted again after Lasley was ruled to have pushed over Rolf Toft as Motherwell scrambled to defend a counter-attack.
The hosts might have had a penalty themselves seconds earlier when Simon Ramsden went down as he looked set to score following a corner.
Stjarnan, who sit second in the Icelandic League after 11 unbeaten games, have the advantage of playing on their own artificial pitch for the second leg of the Europa League second qualifying round.
The visitors had hinted they would sit in, but they pushed four men forward when attacking and Motherwell had a let-off inside four minutes when the unmarked Veigar Pall Gunnarson sent a diving header wide from six yards after the visitors had broken away from defending a corner.
Motherwell forced several more corners and their pressure paid off in the ninth minute as Law scored their first goal in eight European games.
Lasley chipped a cross in for John Sutton, whose header was palmed out by Ingvar Jonsson, and Law had the simple task of knocking it over the line from close range.
Motherwell kept attacking and the second goal came after right-back Niclas Vemmelund slipped on the touchline to concede possession to Iain Vigurs.
Vigurs cut in and played a perfect reverse pass for Law, who dinked the ball over the goalkeeper.
Stuart Carswell should have made it three when Sutton rolled the ball back to him 14 yards out, but the midfielder blazed over.
The visitors were handed a lifeline when Lasley was penalised by Danish referee Michael Johansen as he tried to block a shot with his chest.
Lasley did not protest much as he was booked and Finsen sent Dan Twardzik the wrong way from the spot to the delight of the 22 visiting fans.
Lasley almost made amends by setting up Sutton two minutes later following a one-two with Steven Hammell, but the Englishman shot just wide from 16 yards.
Motherwell finished the half nervously. Reid cleared the danger after some risky defending almost allowed Finsen in, but the right-back then dived in to allow Stjarnan to break and Twardzik got down well to save from Arnar Mar Bjorgvinsson.
Stephen McManus saw a powerful strike saved well after the restart, but Motherwell had another huge scare when Finsen volleyed wide from four yards following a cross from the right.
Vigurs slotted home after a one-two with Law, but a strange offside decision scuppered the celebrations with the flag presumably going up against Sutton, who did not touch the ball.
Finsen came close again with an angled strike from 20 yards and right-winger Bjorgvinsson was causing problems.
But Motherwell had chances to get a two-goal cushion and Jonsson saved well from Lasley before substitute Lee Erwin headed over.
And the injury-time drama nudged the game in Stjarnan's favour.
- Sports & Recreation
- Jamie Langfield
- Jonny Hayes
- Peter Pawlett
- Danny Hoesen
- Keith Lasley
- John Sutton
- Niall McGinn