Montreal were cruising after 52 minutes with left-winger Duka having struck either side of half-time but the Impact could not hold on for a famous win, as Heriberto Olvera and Ariel Nahuelpan levelled the tie ahead of next week's second leg in Canada.
The Impact are in their maiden Champions League campaign and have never before won a competitive fixture in Mexico - the graveyard of many MLS clubs.
Duka gave Montreal the lead in the 25th minute, cutting in from the left before picking out the bottom corner from the edge of the box.
Justin Mapp set up the Impact's second goal, getting inside the penalty area in the 53rd minute and shooting, which caused Pachuca goalkeeper Oscar Perez to parry the ball into Duka's path for a comfortable finish.
But three minutes later Pachuca were on the scoreboard with Olvera's free-kick deflecting off Montreal's defensive wall to loop into the top corner.
The hosts equalised in the 68th minute after a goalkeeping howler by the Impact's Evan Bush, who failed to hold Hirving Lozano's low cross and Nahuelpan bundled the ball across the line with his stomach.
In the other quarter-final first leg, Honduras' Olimpia were held 1-1 at home by Herediano of Costa Rica.
