The Red Warriors had entered Tuesday's game at the Bukit Jalil Stadium with five wins and two draws from their opening seven games.
However, with the quality at Selangor's disposal, the Red Giants were always going to be a match for the champions as long as they found their rhythm, and it was them who took the lead in the 47th minute when talismanic midfielder Safiq Rahim lashed home a blistering effort from outside the area.
Selangor then doubled their lead in the 75th minute when new signing Bosko Balaban timed his run to perfection and raced through on goal, before finishing into the bottom corner.
Kelantan pulled one back at the death when S. Subramaniam capitalised on some hesitant defending to smash home after a goal-mouth scramble, but while it was too little to late for the Red Warriors, they remain top of the league.
Perak are still two points behind Kelantan in second, having missed an excellent opportunity to go top when they fell to a 2-1 loss to LIONSXII, their first at home this season.
Shahril Ishak gave the visitors the lead after he reacted well to Sufian Anuar's nod back to prod the ball home at full stretch ten minutes before the break.
However, Perak came out for the second half looking inspired, and duly equalised in the 49th minute when Michal Kubala smashed home from the spot, after Safuwan Baharudin had felled Lazar Popovic in the box.
Nonetheless, LIONSXII went on to grab all three points 15 minutes from time when Shahril once again found himself in space in the Perak box, and clinically nodded home Shaiful Esah's pinpoint cross.
Terengganu remain third in the league although they will be disappointed after being held to a 1-1 draw by Kedah.
The Turtles took the lead when Ashaari Shamsuddin scored with a cracking left-footed effort from the edge of the box, but Kedah stole a share of the spoils when Amar Rohidan nodded home Abdulfatah Safi's cross from the left.
Terengganu's city rivals T-Team made it two wins on the trot by recording a comfortable 3-0 win over Felda United at the Hang Jebat Stadium, courtesy of a brace from Mohd Faiz Subri and a Zairo Anuar strike.
Sarawak recorded a hard-fought 2-1 win over Johor FC to leapfrog their opponents into 8th place.
The Crocs did not get off to the best start, falling behind in the 21st minute through Arthur Henrique's brilliant 35-yard freekick, but they hit back 12 minutes later when Guy Bwele matched Henrique's effort, albeit from the edge of the area
Johor then had two goals controversially ruled out, before Mohd Azizan Baba bagged the winner for Sarawak when timed his run to the near post to perfection, before nodding home a corner.
Elsewhere, Negri Sembilan and PKNS FC played out a 1-1 draw, while Kuala Lumpur are still looking for their first win of the season after losing 2-0 to Sabah, with goals coming from Mohd Rozaimi Abdul Rahman and Michael Baird.
Tuesday's Malaysia Super League Results
Selangor 2-1 Kelantan
Perak 1-2 LIONSXII
Terengganu 1-1 Kedah
Felda United 0-3 T-Team
Johor FC 1-2 Sarawak
Negri Sembilan 1-1 PKNS FC
Sabah 2-0 Kuala Lumpur