Substitute Padraig McNulty netted the only goal of the contest late on.
Derry were defeated 2-12 to 1-18 by Galway at Celtic Park, Niall Loughlin's late goal proving a mere consolation as their winning league start was ended.
Cavan recovered from a 1-9 to 0-5 half-time deficit to see off Meath 1-20 to 1-13 in Navan, Eamon Wallace and David Givney scoring the goals.
Seanie Johnston was a regular points-scorer for the visitors as they mounted a stunning second-half comeback.
A bad day for Meath was compounded in the latter stages when their goalkeeper Paddy O'Rourke was red-carded.
Laois had not beaten Tyrone in the league in over a decade, and early indications pointed to this game being a tight affair, but ultimately the Red Hands kicked on for victory thanks to a strong second-half display.
Tyrone started brightly with points from Mark Bradley and Darren McCurry, but Laois drew level but he 10th minute, following scores from Paul Cahillane and Gary Walsh.
Tyrone edged in front again by the 14th minute with Barry Tierney placing them 0-3 to 0-2 in front.
However, Laois hit a purple patch, registering four of the next five points with John O'Loughlin taking two fine scores from play during this spell.
Ahead by two points with 11 minutes to go before the interval, Laois looked good, but rued six first-half wides, with Tyrone defending well through the likes of Tierney, HP McGeary and Justin McMahon.
Tyrone ended the half with four unanswered points, with Ronan O'Neill and Tiernan McCann on target to level the tie in the 27th minute.
Despite Tyrone also being wasteful with seven first half wides, they took the lead at the break.
The visitors shaded a 0-8 to 0-6 interval lead, with late points from Niall Sludden and O'Neill in injury-time.
Tyrone added a further four unanswered points on the restart, as they totally controlled proceedings.
O'Neill and Tiernan McCann added to their tally, while Mattie Donnelly registered two fine back-to-back scores from play, as Mickey Harte's side powered to a double-scores 0-12 to 0-06 lead.
Laois's first score in 20 minutes arrived from the boot of John O'Loughlin, but Tyrone were sharper.
An injury to Ronan O'Neill halted Tyrone's momentum, with a score from Laois substitute Ruairi O'Connor cutting the gap to five points entering the final quarter.
Donnelly and Donal Kingston traded points, before less than a minute after his introduction McNulty had the ball in the Laois net to ensure a 1-14 to 0-09 lead.
Indeed Laois kicked five unanswered points in response to the Dungannon clubman's goal, with brothers Donal and Paul Kingston on target.
However, Tyrone held out to claim a deserved win, with keeper Michael O'Neill denying an equalising goal from Niall Donoher, after a well-placed save, and an O'Connor late scoring chance blocked.
Derry went into their game unbeaten after victories over Fermanagh and Cavan, but without manager Damian Barton on the sideline after he was handed an eight-week suspension.
Five unanswered points helped Galway to a 0-6 to 0-2 lead by the 15th minute and the visitors enjoyed a 0-10 to 0-7 advantage at the interval.
Adrian Varley scored a goal with an emphatic finish into the roof of the net three minutes into the second half to emphasise Galway's superiority.
The Oak Leafers came with a late flurry, thanks to Ryan Bell's sixth point of the day and Loughlin's goal, but their opponents ran out three-point victors.
Tyrone kept up their unbeaten run with a 1-14 to 0-14 Football League win over Laois in Division Two in Portlaoise.