Stefan Campbell who led the Armagh charge with seven points.
It was a second defeat in a row, but Armagh did show their battling qualities with a rewarding second half comeback that just fell short at the end of the tussle.
Still smarting from their defeat by Galway last week, the visitors went into the break ahead.
Armagh had made a decent start with Stefan Campbell hitting three frees, but a huge turning point came on 13 minutes when Paul Cahillane struck a penalty to put his side ahead and they were to hold onto this advantage to the end.
Laois continued to tot up the points before Armagh finally got into their stride in the last quarter.
Campbell hit seven points as the home side staged a strong rally, but Laois being reduced to 14 men they held on for a narrow victory.
The defeat pushes Armagh into relegation trouble with the next game again at the Athletic Grounds against Down on Sunday, February 14 at 2.00pm.
Scorers for Armagh – S Campbell 0-7 (4f), M McKenna 0-3, E Rafferty 0-1, A Forker 0-1, G McParland 0-1 (f), S Heffron 0-1, N Grimley 0-1. Laois – P Cahillane 1-2 (pen, 2f), D Kingston 0-5 (3f), E O’Carroll 0-3 (one ‘45’), M Campion 0-1, N Donoher 0-1, G Walsh 0-1 (f)
ARMAGH: M McNeice; S Heffron, C Vernon, R McCaughey; S Forker, A Forker, M Shields; A Findon, S Sheridan; S Campbell, M McKenna, N McConville; C Watters, C O’Hanlon, G McParland.
Subs: E Rafferty for McConville (HT), E McVerry for McParland (46), N Grimley for Sheridan (50), J McElroy for S Forker (60), O MacIomhair for Watters (62), S Connell for McCaughey (68).
LAOIS: G Brody; R Kehoe, M Timmons, D Seale; D Strong, P Cotter, G Dillon; K Lillis, K Meaney; J Farrell, D Kingston, N Donoher; P Cahillane, E O’Carroll, G Walsh.
Subs: M Campion for Meaney (17), A Farrell for Cotter (BC, 33), D O’Connor for Strong (52), D O’Reilly for Walsh (55), R O’Connor for Campion (58)
REFEREE: Barry Cassidy (Derry)