Two tries in the opening quarter by Tulsen Tollett and Steve Rosolen gave London an early cushion and the lead was doubled just before the break by another pair of tries, this time from Greg Barwick and Darren Shaw.
Leeds, 24-0 down at the interval, made a fight of it in the second half and tries from David Hulme and Marcus St Hilaire reduced London's lead to 12 points.
However, Barwick, who finished the game with 17 points from a try, six goals and a drop goal, kicked a 50-yard penalty and then Russell Bawden dived over from close range.
Castleford Tigers snatched a dramatic 36-31 win against Sheffield Eagles at Wheldon Road with a late try from centre David Chapman.
Sheffield were 31-30 ahead with only two minutes left when Chapman went over in the right-hand corner, Frano Botica adding his sixth goal.Reuse content