Both teams adopted cautious formations and the visitors made the breakthrough on 32 minutes when Niger-born striker Kamilou Daouda scored with a fine header.
The potentially crucial goal in the first leg of the semi-final followed a fine cross from flying winger Baba Ousmaila.
Dynamos could have led as early as the seventh minute but after dribbling past several defenders, striker Benjamin Marere failed to beat Cotonsport goalkeeper Daouda Kassali.
Cotonsport had the ball in the net after 25 minutes through captain Ahmadou Ngomna, but the effort was disallowed as he used his hands instead of his head and was shown a yellow card.
Daouda’s goal was his sixth this year in the competition, still far behind 13-goal leading scorer Stephen Worgu from Nigerian club Enyimba.
Dynamos goalkeeper Zondai Nyaungwa, standing in for the suspended Willard Manyatera, should shoulder some blame for the only goal as he failed to effectively deal with the cross.
The Harare glamour boys had to contend with opponents who continuously massed 11 players behind the ball as promised by coach Alain Oumbeldon before a match that drew a capacity 35 000 crowd to Rufaro Stadium.
“We came here to get a good result against a team that plays so well at home as evidenced by their victory over Egyptian club Zamalek a couple of weeks ago,” the Ivory Coast-born coach said.
Although Dynamos poured forward in search for an equaliser, forcing nine corners, their strikers either shot wide or were foiled by impressive defending.
Captain Murape Murape could have equalised on 62 minutes, but his overhead kick inside the penalty box flew over with only Kassali to beat.
During the second half, Cotonsport became more adventurous with Ngomna, initially a defensive midfielder, starting to push forward as the club from the northern town of Garoua sought a tie-clinching second goal.
The return match will be staged at the Omnisport Stadium in Garoua over the weekend of October 17-19 with the winners advancing to a two-leg final next month.
At the Aba International Stadium, Egyptian giants, Al-Ahly held two-time winners, Enyimba to a goalless draw in the other second leg clash.
The Nigerian hosts went into the game with a fine home record, but despite applying most of the pressure, they were wasteful in front of goal.
Enyimba had won every home game in the group stages, scoring 10 goals and conceding only one.
Al Ahly played as a well-organised unit, and were aiming for a goal on the break, although it was not to come.
Their best chance came in the 78th minute when Mohamed Aboutrika got to the end of a poor back pass by Chinedu Ezimorah, but goalkeeper Sani Haliru made a save.
With six minutes remaining, Enyimba substitute Emeka Akueme misdirected a free header inside the six-yard box with the Egyptian defence well beaten.
Three years ago Ahly managed a 1-0 win in Aba in the group stage of the competition.