With UEFA Champions League (UCL) qualification a genuine possibility for both sides, there was plenty at stake here, emphasised by an energetic start to the contest.
Starting up front for Fulham, Rodrigo Muniz hadn’t scored in any competition since the opening Premier League weekend, and he should have done better when directing his firm header the wrong side of the near post.
Clear-cut chances had been at a premium when the momentum threatened to swing in the hosts’ favour, with Bournemouth reduced to 10 men thanks to a studs-up challenge from Ryan Christie on Timothy Castagne.
The Cottagers almost made their numerical advantage immediately count, but Joachim Andersen could only find the crossbar with his header from Harry Wilson’s inswinging cross.
The first shot on target of the half didn’t arrive until Sasa Lukic tested Dorde Petrovic from range in stoppage time, yet there was still time for more drama as Andersen’s season came to an abrupt end following a straight red card - Fulham’s first of the season - for a reckless tackle on Adrien Truffert.
Goalless at the break, it looked to be an open second period with both sides depleted, and within eight minutes of the restart, the deadlock was broken.
Bournemouth were the side on the front foot, coming close when Eli Junior Kroupi bent an effort onto the crossbar from the edge of the box, and from a similar position, Rayan went one better, sending a bouncing strike beyond Petrovic for his third goal in as many matches.
Fulham have now kept just one clean sheet in 11 home games, and having failed to score in six of their last eight in all competitions heading into this, had a real task on their hands.
The hosts pushed for a leveller, yet it was Rayan who almost grabbed the game’s second after a lung-busting run had the Cottagers panicking.
Substitute Amine Adli then miskicked with the goal at his mercy, before Josh King rattled the underside of the crossbar at the other end in stoppage time, ultimately keeping the scores level.
A first win in five trips to Fulham (D3, L1) to keep Andoni Iraola’s side sixth, closing the gap on Aston Villa to three points, albeit having played a game more. Nonetheless, sixth place may well be enough to secure UCL football should the Villans stay fifth and go on to win the UEFA Europa League.
The prospect of claiming a spot in Europe’s premier competition is now over for Marco Silva’s side, yet some form of European qualification remains possible, especially ahead of a trip to bottom-side Wolverhampton Wanderers.