The former Chelsea striker opened the scoring with his second goal of the season just nine minutes into the match, curling a stunning free-kick into the bottom left corner of the net after Ignacio Piatti had been fouled on the edge of the box.
The Impact could not hold onto their lead, however, as Shkelzen Gashi made it 1-1 just after half-time when he finished off a low cross from Mekeil Williams.
Maxime Tissot put the hosts back in front three minutes later with a long-range blast, but Rapids defender Bobby Burling levelled things up again in the 73rd-minute to ensure they returned to the States with a point.
It was certainly a missed opportunity for Montreal after largely dominating proceedings on the day, but head coach Mauro Biello was nevertheless quick to single out Drogba for praise after the final whistle.
The 38-year-old Ivorian was playing in his third full game in only eight days after making just two substitute appearances over the club’s opening six matches in order to avoid artificial turf, and while he had been dealing with a cold during the week, he still looked fit and threatening throughout the 90 minutes.
“With Didier he’s been congested all week and he just had a little bit of trouble breathing because he has a bit of a cold, but he fought through it,” Biello told goal.com after the match. “This was a good week for him in terms of getting his fitness and he scored a great goal for us; he did a ton of work on the defensive side, helping us with set pieces.
“For this fitness were happy that he’s played these three games and he’s only going to get better from here.”
Drogba signed an 18-month deal with the Impact last summer after his ending his second spell at Chelsea and went on to score 11 times in 11 regular season games as the club secured a third place finish in the East.
The veteran forward subsequently added another goal to his tally in the 3-0 first-round playoff win over Canadian rivals Toronto FC, before his side’s hopes of a maiden MLS Cup title were dashed with a narrow 4-3 aggregate defeat to Columbus Crew SC in the Conference Semifinals.
After coming close to re-joining Chelsea in a backroom role over the winter, the Blues legend’s contributions have been limited so far this term, but his absence over the opening weeks does not seem to have hurt the Impact too much.
The draw with Colorado leaves them sitting top of the Eastern Conference with 14 points from nine games, having recorded four wins two draws and suffered just two defeats.