The Etixx-QuickStep rider finished ahead of Movistar’s Alejandro Valverde and Australian Michael Matthews (Orica-GreenEDGE) to win the first of a tryptich of races in the Ardennes.
"This was a great day for me, the hard work paid off," said Kwiatkowski.
"I'm really thankful that my team-mates were so amazing today. I was always in the top 20 or 25 positions. I could relax the whole day. We had Tony (Martin) in the important breakaway and that was crucial for me. Of course I was suffering as well in a race with so many climbs.
The second-to-last time up the Cauberg I said to Gianni Meersman 'you know, I'm not feeling so good today.' But he said to me straight away that everyone is suffering with 34 climbs at this race and I have to make it. That gave me a lot of motivation before the last time up the Cauberg. I'm really thankful they believed in me until the last moment. In cycling you never know what to expect from those around you. You might look around and feel like no one is suffering but you, but you don't know the true situation until the last important acceleration.
"For the sprint I was able to sit in the slipstream and breathe a little bit, and that was important to recover from the effort on the Cauberg. I was able to get some energy back to go full gas in the select group sprint and win Amstel Gold Race."
Laurens De Vreese (Astana), Jan Polanc (Lampre-Merida), Timo Roosen (LottoNL-Jumbo), Linus Gerdemann (Cult Energy), Johann Van Van Zyl (MTN-Qhubeka) and Mike Terpstra (Roompot) got the ball rolling with the break of the day.
The six riders went early but were kept under control by the unhurried peloton for two climbs of the Cauberg with a lead that declined from a high of 10 minutes to less than six at the second passage.
With less than 50km to go Polanc, De Vreese and Gerdemann distanced the other three riders in the break while behind in the peloton things grew heated as the climbs, tight roads, road furniture and speed combined to place several riders in a precarious position.
The tension was evident when Vicente Reynes (IAM) and Roy Curvers (Giant-Alpecin) exchanged light blows, remonstrations and colourful language when the the peloton hit a traffic jam on one of the tight steep climbs.
With the time gap narrowed to less than a minute an attack out of the peloton by Australians Simon Clarke (Orica-GreenEDGE) and David Tanner (IAM) joined and later dropped Polanc, De Vreese and Gerdemann.
An aggressive Vincenzo Nibali (Astana), Tony Martin (Etixx-QuickStep) and Alex Howes of Garmin-Cannondale also escaped the clutches of the peloton to form a second dangerous group which eventually bridged to Clarke and Tanner.
With Nibali agitating, that combination went on to hold a narrow 15 second lead with 18km left to race as the peloton led by BMC ramped up the speed to bring them back.
The collective effort lasted until the 8km to go mark with Clarke the last of the five to succumb to the pressure after dangling solo for several kilometres.
The peloton came together for a final assault on the Cauberg where individual strength would force the final winning selection.
Defending champion Philippe Gilbert (BMC) was the first to make a move but he was closely marked by a determined Matthews as a larger group which included Kwiatkowski and Valverde fought their way into contention.
BMC made the first move then Sky as the race became a mass sprint with tired legs. But it was Kwiatkowski, the rider who had done the least amount of work throughout, who was the freshest at the finish.
Amstel Gold Race: 251km, Maastricht to Valkenburg
1 Michal Kwiatkowski (POL) Etixx-QuickStep 6hr 31min 49sec
2 Alejandro Valverde (ESP) Movistar
3 Michael Matthews (AUS) Orica GreenEDGE
4 Rui Costa (POR) Lampre-Merida
5 Tony Gallopin (FRA) Lotto-Soudal
6 Greg Van Avermaet (BEL) BMC
7 Julian Alaphilippe (FRA) Etixx-QuickStep
8 Enrico Gasparotto (ITA) Wanty-Groupe Gobert
9 Maciej Paterski (POL) CCC Sprandi Polkowice
10 Philippe Gilbert (BEL) BMC