Duka drove past two Pachuca defenders and took a shot from just outside the penalty area in the 25th minute. He added his second of the match in the 53rd minute.
Pachuca's Ariel Nahuelpan Osten tied the game in the 68th minute. Heriberto Olvera scored on a free kick in the 57th to cut Montreal's lead to 2-1.
It was the opening match of the season for the Impact, who host Pachuca in the second leg of the quarter-final next week.
"We have a fresh team and it's a fresh start with a group of leaders with experience and young players," said Duka.
The winner of the two-leg, home-and-away series is determined by aggregate goal differential, with the advantage given to the side that scores more goals on the road if they are tied after the two matches.
"For our first match in 2015, it's a very good result," said Impact head coach Frank Klopas. "We played against a very good team and two goals scored on the road in Mexico are very good. They did not know much about us before tonight, but it will be different in the second leg.
"The mentality and work ethic have been great. I am happy with the performance of the group. We played as a team tonight. It was also nice to see the fans that made the trip."
Montreal is one of two MLS teams to have advanced to the CONCACAF quarter-final stage. The other is D.C. United.