Disasi prodded home from close range when an Ismail Jakobs free-kick fell to him in the penalty area 10 minutes from time at the Stade Louis II. That cancelled out Joey Veerman's first-half opener for PSV and ensured the tie is finely poised ahead of next week's return leg in the Netherlands.
Former PSV striker Van Nistelrooy was appointed as coach of the former European Cup winners ahead of this season and oversaw a 5-3 victory against Ajax in the Dutch Super Cup last weekend. His team got off to an ideal start in the principality as they went ahead seven minutes before the break when skipper Luuk de Jong laid the ball off for Veerman to sidefoot home with a clinical finish into the corner from the edge of the box.
Japan star Takumi Minamino, making his competitive debut for Monaco after signing from Liverpool, fired just wide at the start of the second half as the hosts went in search of an equaliser. The goal arrived through Disasi from a set-piece in the 80th minute and Monaco could even have won the game as Youssouf Fofana headed against the post from close in with two minutes remaining.
The second leg will be in the Netherlands next week, with the winners going on to face either Union Saint-Gilloise or Rangers in the play-offs later this month, seeking the reward of a berth in the highly lucrative group stage.
Monaco missed out on direct qualification for the group stage when they conceded a stoppage-time goal on the final day of the last Ligue 1 season and dropped from second to third in the table as a result, behind Marseille. They were denied a place in last season's Champions League group stage when they lost to Shakhtar Donetsk in the play-offs.
Rangers, last season's beaten Europa League finalists, faced Union Saint-Gilloise in Brussels in the first leg of their third qualifying round tie, losing 2-0, as they look to return to the Champions League group stage for the first time in over a decade. Benfica, who reached the quarter-finals last season before losing to Liverpool, faced Midtjylland of Denmark, winning 4-1 at the Estadio da Luz.
Earlier there were 2-1 away wins for Viktoria Plzen of the Czech Republic, and Croatia's Dinamo Zagreb, against Sheriff Tiraspol of Moldova and Ludogorets of Bulgaria respectively. Dynamo Kyiv will play on Wednesday but the Ukrainian club will play the home leg of their tie against Austria's Sturm Graz in the Polish city of Lodz due to the ongoing conflict in their country.