Richardson scored a magnificent individual goal just before half-time, the right-back's first goal for 20 months.
Then Marques, playing his last game before reporting for African Cup of Nations duty with Angola, headed the second in the 52nd minute.
Leeds had Neil Kilkenny making his debut after signing him initially on loan from Birmingham City with a view to a permanent transfer and the Australian showed some intelligent touches in midfield.
Paul Huntington also impressed in his first league start and Tore Andre Flo started for the first time in nearly a year, with Tresor Kandol demoted to the bench.
However, Peter Sweeney's arrival from Stoke City came too late to enable the former Scotland Under-21 international midfielder to play.
Northampton were without Bradley Johnson who is expected to join Leeds United next week after the clubs agreed a fee believed to be in the region of £250,000.
Town made their intentions clear by packing the midfield and leaving Andy Kirk as a lone striker.
They had a big let-off in the 23rd minute when Huntington's excellent throughball set up Jermaine Beckford. Keeper Mark Bunn blocked Beckford's shot and Flo drove the ball low for Brett Johnson to clear off the line.
Leeds found it difficult to penetrate the visitors' massed ranks, but their patience paid off two minutes before the break when Richardson set off on a long diagonal run before shooting past Bunn from just outside the penalty box.
Marques added the second when Andy Hughes turned Kilkenny's corner back into the goalmouth and Beckford was denied three times by dogged defending and the bar before Weston shrugged off Mark Hughes' tackle to steer the ball in for the third.