Fulham, who had held the Gunners to a goalless draw at Highbury earlier in the season, made a real go of taking on the champions but were undone by a terrible mistake from goalkeeper Edwin van der Sar.
He gifted Reyes a goal after only nine minutes and although the home side created a string of opportunities after that, they could not recover.
Now, with only one game remaining this campaign, a clearly tiring Arsenal side are within touching distance of remaining unbeaten all season.
But Fulham must be frustrated that they didn't get at least something out of this match, which was their last ever game at Loftus Road before returning to Craven Cottage next season.
Van der Sar's terrible mistake gifted Arsenal the lead after only nine minutes and in the end cost Fulham everything.
The Dutch keeper had plenty of time when he took a Martin Djetou back-pass in his stride. But instead of releasing the ball he dallied and then lost out in a weak tackle with Reyes - allowing the Spaniard to tap home from three yards.
It was a major embarrassment for Holland international van der Sar, who has recently been linked with a summer move to Highbury.
But in a rather disjointed match it was a rare highlight in a first half that failed to live up to expectations.
Fulham wasted a chance to level the scores almost immediately when Luis Boa Morte was put through but saw his effort blocked by the body of keeper Jens Lehmann. Steed Malbranque missed from the rebound and that was the end of the chances for the first half.
Fulham came close to equalising in spectacular fashion in the 56th minute, when Malbranque's overhead kick from a Sean Davis cross fizzed only narrowly over the bar.
Then Sylvain Legwinksi saw his 20-yard shot blocked following a flying run from Boa Morte.
In truth there was little pace or urgency to the game and neither side was able to dominate possession for long. But Fulham did have the better chances and Moritz Volz fired agonisingly wide in the 78th minute.
Malbranque also wasted a free-kick right on the edge of the area and couldn't quite get his toe on the ball in one of several penalty-box scrambles.
As for Arsenal, they rarely got out of first gear with Thierry Henry especially quiet - except for one dazzling run and a free-kick that was saved in the last minute.
But nobody at Highbury will be worried about that. All that matters is that the Gunners are only one match away from a remarkable achievement.