World champion Kwiatkowski was able to hold off Movistar's Alejandro Valverde and Matthews on the Cauberg to win the Amstel Gold Race.
The result is the second Monument podium of the season for 24-year-old Matthews who also finished third in Milan-San Remo.
“For my first time attempting the final at Amstel, I have to be happy with the result,” Matthews said. “I’m happy with the way I rode, I left everything out there. It’s just unfortunate that it wasn’t for the victory.”
“I went quite deep to follow (former winner Philippe) Gilbert on the climb and I used a lot of energy trying to stay with him. I thought going over the climb we were clear of everyone else but the bunch had a few too many guys and were able to come back to us.
“I was hoping it was going to be just Gilbert and I in the sprint because I was quite confident in that situation but in the final sprint I just had nothing left and it was just a grovel.”
Orica-GreenEDGE sports director Matt White was full of praise for the team.
“We went in with a plan of how we wanted to attack the race and the guys did it to perfection,” said White.
“Gilbert is renown for going on the Cauberg. The years he has gone clear he has stayed away to win so that was our plan, to give Michael as much protection as possible during the day so he was able to go with Gilbert on the last climb.
“He had the advantage of a well-drilled team including Simon Gerrans, who has podiumed here in the last two years, and that sort of firepower is invaluable.
“Michael was able to react to the Gilbert move on the climb and he gave himself every chance for the win.”