Langer, who almost missed the Darwin game after being struck on the foot during practice on Wednesday, batted for five hours, facing 256 balls and hitting 13 fours and a six. It was his 64th first-class century.
He shrugged off his injury. "I got up every couple of hours last night and iced it....so I'm more tired today than (having a) sore foot," he said.
The left-hander, offered one of his extra lives in the 90s, steadied the home team during a third-wicket partnership of 181 with Rhett Bowden.
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The uncapped 20-year-old was the pick of the bowlers with four for 75 from 19 overs while leg-spinner Upul Chandana chipped in with two wickets after conceding 104 runs from 20 overs.
Sri Lanka coach John Dyson said of Malinga: "He's a pocket rocket."
"Early on he bowled very well and he shocked a couple of blokes. Every time he got the ball he bowled it with enthusiasm and pace and something looked like it could happen."
"If he continues this innings and then bowls again really well in the next innings he could come into serious consideration for the Test."
But with world record holder Muttiah Muralitharan opting to skip the tour, the Sri Lankans failed to capitalise on their great start against a team made up of local amateur players but captained by Langer and strengthened by the inclusion of Katich and Glenn McGrath.
Sri Lanka briefly halted the run flow when Chandana removed Bowden and Ashley Williams and Ken Skewes followed quickly but Langer once again took control.
He took the total along to 274 before he was bowled by Farveez Maharoof. Martin Brown (45) and Darren Treumer (49 not out) added 90 for the seventh wicket.
The four-day match is Sri Lanka's only warm-up before next month's two Tests in Darwin and Cairns.
Scorecard:
Northern Territory first innings
J.Langer b Maharoof 151
I.Redpath c Sangakkara b Malinga 0
S.Katich c Jaywardena b Malinga 0
R.Bowden c Samaraweera b Chandana 75
A.Williams st Sangakkara b Chandana 1
K.Skewes b Malinga 0
M.Brown c Maharoof b Malinga 45
D.Treumer not out 49
A.Dent not out 0
Extras (nb-31 b-6 lb-5 w-1) 43
Total (for seven wickets, 90 overs) 364
Fall of wickets: 1-2, 2-4, 3-185, 4-208, 5-210, 6-274, 7-364
To bat: T.Bayly, G.McGrath, G.Brautigam.
Bowling: Maharoof 20-1-65-1 (nb-13 w-1), Malinga 19-2-75-4 (nb-14), Fernando 17-1-63-0 (nb-4), Herath 9-2-35-0, Chandana 20-2-104-2, Jayasuriya 5-1-11-0.
Sri Lanka: M.Jayawardena (captain), S.Jayasuriya, K.Sangakkara, T.Samaraweera, T.Dilshan, R.Arnold, R.Kaluwitharana, U.Chandana, D.Fernando, F.Maharoof, R.Herath, L.Malinga.
