The Swede headed in an inviting free-kick from Pawel Cibicki, who produced an impressive debut performance at Elland Road, to settle the issue as United’s revival after the last international break gathered apace.
Norwich went close in the second half during spells of pressure, but United dug deep to get over the line and secure a sweet three points in the process.
Previous visits to Yorkshire this season had seen Norwich afford both Sheffield United and Middlesbrough plenty of frustration en route to single-goal wins, but thankfully developments just before the interval ensured that the feeling among Leeds supporters was rather more favourable at the break.
It was due to a second goal in successive home games for Jansson, with the big Swede glancing in an inviting free-kick from Cibicki, who fully justified his first start at Elland Road by virtue of some sweet set-piece deliveries.
In truth, it was a half of few clear-cut opportunities, with Leeds far from at anywhere approaching their best.
But their perseverance was still admirable in the circumstances on an afternoon when patience soon looked like being a virtue.
Well organised without the ball, Norwich kept their discipline for the most part throughout a pretty tepid first period, but fatally blinked with the interval approaching.
Moments before Jansson’s strike, the visitors suffered their scare when another quality set-piece delivery, this time from Ezgjan Alioski, saw Kalvin Phillips get a connection and prod a close-range effort against the post with Cibicki’s follow-up blocked.
It was a warning which was not heeded.
Earlier, the game resembled a bit of an arm-wrestle, with a pot-shot from distance from Gaetano Berardi flashing wide representing the most dangerous moment.
After offering little in an offensive sense, the Canaries saw their best opportunity arrive after falling behind and it should have yielded a leveller.
It saw James Maddison wastefully fire a rebound over with a clear sight of goal following Felix Wiedwald’s unconvincing parry to turn away Nelson Oliveira’s low curler.
After a pragmatic first half, the onus was on Norwich to be more proactive on the restart and they started the second period with much more urgency.
It should have led to a leveller early in the second half with Alex Pritchard, afforded plenty of space after Liam Cooper failed to cut out Marley Watkins’ cross from the left, denied by a smart near-post block by Wiedwald, with the goal gaping
Maddison soon saw his deflected shot held by Wiedwald as the Canaries pressed again, with the hosts struggling to get going at the start of the half, but with the insurance policy of a precious lead.
Leeds gradually found some tempo, with Gunn turning away Samuel Saiz’s rasping drive before a howitzer from Kalvin Phillips flashed just wide as the hosts sought a killer second.
It was the prelude to a lively final half-hour not in keeping with the opening sixty minutes and while Norwich certainly had their moments, United dug in and showed a strong team ethic to get over the line.
An altercation between Jansson and Nelson Oliveira saw both players booked after the home defender had made a fine initial challenge to deny the City frontman before Pritchard went desperately close to a leveller with his curler clipping the top of the woodwork.
Wiedwald then denies the increasingly influential Pritchard before play swung to the other end with Saiz having a gilt-edged chance to seal it after Grant Hanley’s woefully-short back pass, with his precision low shot striking the base of the post.
Marley Watkins then fired inches wide ahead of a frenzied finale which incorporated six minutes of stoppage-time.
Sub Pablo Hernandez went close to a second right at the death, but one goal was enough
Leeds United: Wiedwald; Ayling, Jansson, Cooper, Berardi; Phillips, Vieira; Cibicki (Pennington 85), Saiz (Grot 81), Alioski; Roofe (Hernandez 78). Substitutes unused: Lonergan, Shaughnessy, Anita, O’Kane.
Norwich City: Gunn; Pinto, Hanley, Klose, Stiepermann (Hoolahan 83); Reed, Vrancic (Jerome 83); Pritchard, Maddison, Watkins; Oliveira. Substitutes unused: McGovern, Zimmermann, Murphy, Trybull, Tettey.
Referee: D England (South Yorkshire).