PSG started their latest title defence with back-to-back defeats but have now won three games in a row without conceding.
Icardi put the champions in front against out-of-form Reims with a clinical finish past Predrag Rajkovic inside nine minutes and added a second with a little over an hour played.
Thomas Tuchel's side had further opportunities to extend their lead but in the end two goals were enough against a Reims side still without a win this term.
Kylian Mbappe was denied by Rajkovic after six minutes but he played a big part in PSG's opener by slipping the ball through for Icardi to control and fire into the far corner.
The visitors, beaten in their last two meetings with Reims, nearly added a second through Angel Di Maria's drive and Icardi's saved header in the space of two minutes.
Neymar also went close to doubling his side's tally with a mazy run that ended with the superstar forward firing a shot past the far post from inside the six-yard box.
Those wasted chances did not come back to haunt Tuchel's men, though, as Icardi converted Mbappe's squared pass to round off a fine team move with 62 minutes gone.
Mbappe should have added some gloss to the scoreline late on but was guilty of a horror miss, somehow firing wide with plenty of the unguarded goal to aim for, while substitute Pablo Sarabia also blazed over an effort from inside the box.
What does it mean? Three and easy for PSG
It is now three wins in a row for PSG without conceding, moving them up to seventh in the table and within four points of early pacesetters Rennes.
The champions may only have managed two goals from 21 attempts, but the victory is all that counts and Tuchel will be hoping to maintain this momentum.
Icardi leads from the front
Former Inter frontman Icardi spearheaded an attacking PSG line-up that also included Neymar, Mbappe, Di Maria and Julian Draxler.
He scored both goals to get off the mark for the season and also created four chances for his team-mates in an impressive all-round display.
Mbappe misses a sitter
The victory was never in doubt for dominant PSG, but they should have won by an even more convincing margin.Mbappe was teed up by Sarabia but contrived to miss from close range, although the France international did lay on both assists for Icardi and - that miss aside - can be pleased with his performance.
Reims head to league leaders Rennes for their next outing in a week's time, while PSG host Angers on Friday.