Jansson’s found the net four minutes before half-time, glancing home a Pawel Cibicki free-kick, as United continued to close in on the Championship’s top six.
Leeds had toiled through much of the first period, despite dominating Norwich at Elland Road, but Jansson’s effort - nodded in off a post - came seconds after Kalvin Phillips had driven a volley against the opposite upright.
Both sides were denied by the woodwork in an engrossing second half and United came under the cosh as the game wore on but Christiansen’s side held out to register another success.
The result took advantage of points dropped by Sheffield United and Aston Villa elsewhere, placing Leeds within touching distances of a play-off place with the season almost at the halfway stage.
Norwich’s early confidence belied their low league position and Leeds were denied much possession initially but Phillips saw the first sight of goal with a curling shot beyond Angus Gunn’s far post.
United felt their way into the game as the first half developed but neither goalkeeper was forced into a save until the 18th minute when Alex Pritchard pounced on a sliced clearance from Felix Wiedwald, producing a shot which Wiedwald got behind and brought under control.
United head coach Thomas Christiansen named the German in goal again despite his error against QPR last weekend and Cibicki was handed a full league debut ahead of Pablo Hernandez after a strong display as a substitute at Loftus Road.
The Swede almost fashioned a goal on 25 minutes when his low ball into City’s six-yard box narrowly evaded Kemar Roofe and Gaetano Berardi was inches away from a first career goal with a 30-yard shot which crashed wide.
Luke Ayling then failed to put away a free header from a Cibicki free-kick, directing the ball into Gunn’s arms, but it took a timely sliding tackle from Phillips to stop James Maddison sticking away a close-range opening on 35 minutes.
Phillips, however, rattled a post on 41 minutes and as City struggled to ease the strain, Jansson leapt to bury Cibicki’s cross.
Norwich almost snatched an equaliser in injury-time when James Maddison fired over the bar after Wiedwald parried out Nelson Oliveira’s shot and Wiedwald produced a superb point-blank save from Pritchard as City threatened at the start of the second half.
United fought to limit the visitors’ chances and Phillips and Samuel Saiz both came close to a second goal from long distance after the hour but Norwich dispensed with caution late on and Pritchard was unlucky to see an inventive strike on 74 minutes smash against Wiedwald’s crossbar.
Saiz, though, should have killed the clash 10 minutes from time when Grant Hanley’s weak backpass left him one-on-one with Gunn. The Spaniard drew the keeper but was denied when his delicate finish hit the inside of the far post.
Leeds United: Wiedwald, Ayling, Cooper, Jansson, Berardi, Vieira, Phillips, Cibicki (Pennington 85), Saiz (Grot 81), Alioski, Roofe (Hernandez 78). Subs: Lonergan, Shaughnessy, Anita, O’Kane.
Norwich City: Gunn, Pinto, Hanley, Klose, Stiepermann (Hoolahan 84), Reed, Watkins, Maddison, Pritchard, Vrancic (Jerome 84), Oliveira. Subs: McGovern, Zimmermann, Murphy, Trybull, Tettey.