The Championship side led 6-0 and 12-10 and were only eight points adrift before Leeds took control with four tries in 15 minutes either side of half-time.
The concern for Rhinos was the loss of captain Danny McGuire to an ankle injury in the first half and some sloppy defence which allowed London to run in five tries.
With Rob Burrow sidelined due to a calf injury, Rhinos boss Brian McDermott named Joel Moon at scrum-half for the first time in his Leeds career.
That allowed Jimmy Keinhorst to make a start in the three-quarters.
Jordan Lilley returned on the bench, as did Anthony Mullally and Mitch Garbutt was promoted into the starting front-row.
Lilley and Mullally both turned out for Featherstone Rovers on dual-registration in the regular season, but are now ‘club-tied’ and ineligible to play for anyone other than Leeds for the rest of this season.
The same applies to Ashton Golding, who played for Rhinos under-19s in midweek and was 18th man against London.
The hosts went ahead after five minutes when Rhys Williams picked up a loose ball to race over after William Barthau’s ankle tap had kept Kallum Watkins out.
Jamie Soward converted, but on 12 minutes Tom Briscoe got Leeds on the scoreboard from Watkins’ pass after Carl Ablett, McGuire and Brett Ferres had handled.
There was no conversion, but Rhinos went ahead in the next set. Moon made a break, Keinhorst carried it on and Liam Sutcliffe was in support.
He added the extras, but London were back in front a minute into the second quarter, James Cunningham picking up from acting-half and weaving over from 30 metres out.
Soward added the extras and it took a superb tackle from Keith Galloway, which forced Barthau to loose possession, to keep Leeds’ line intact moments later.
On 26 minutes Briscoe went over for his second try in similar fashion to his opener and Leeds’ nerves were calmed just before the interval when Ablett, Lilley and Adam Cuthbertson carved out a try for Segeyaro, which Sutcliffe improved.
Watkins could have made the game safe two minutes into the second half after storming over the line, but a crunching tackle from Ben Hellewell forced the ball loose before he could touch down.
Six minutes after that Ferres’ kick rebounded off a defender and Lilley picked up to scoot over.
Soward failed to find touch with a penalty and Mitch Achurch scored in the next set, the restart went dead and Watkins crossed following the penalty off a superb pass by Ferres.
Sutcliffe converted the Achurch and Watkins tries to make it 36-12.
London struck back through a Nick Slyney try, improved by Soward, on the hour.
Briscoe scored his hat-trick try, from another Watkins pass and Sutcliffe’s fifth goal completed Leeds’ scoring 17 minutes from time and London ran in late touchdowns through Iliess Macani and Elliot Kear, Soward converting the latter.