Armagh defender Aidan Forker and Louth's Anthony Williams were sent-off early in the game.
Goals from Ciaran McKeever and Rowland helped Armagh to a 2-5 to 0-6 half-time lead and Jamie Clarke added the third.
Antrim eased their relegation worries with CJ McGourty netting in a 1-10 to 0-11 win against Laois, who had Damien O'Connor red-carded before half-time.
Conor Murray scored two points at Corrigan Park as the Saffrons moved into an early 0-4 to 0-1 lead, but Ross Munnelly and David Conway were on target as Louth levelled.
The decisive period in the game came just before the break with McGourty's goal and the dismissal of O'Connor.
Antrim led 1-5 to 0-6 at half-time but Laois levelled on the restart thanks to points from Ambrose Doran and Alan Farrell.
Paddy McBride restored the host's advantage only for James Finn to make it all-square again.
CJ McGourty slotted over three of Antrim's final four points as they edged clear to clinch a valuable win to leave the Ulster side sixth in the standings.
"If we didn't get the two points from this game we would be up against it," said Antrim joint-manager Gearoid Adams.
"CJ McGourty led by example with pressure frees and we got over the line - we must push on now."
There was a dramatic opening at the Gaelic Grounds with Forker red-carded after 50 seconds followed by McKeever's goal and the exit of Williams on 10 minutes.
The Orchard visitors made a blistering start, surging to a 2-3 to 0-1 lead with Rowland firing in the second goal.
Louth pair Paraic Smith and Ryan Burns each scored three first-half points and the Division Three pacesetters trailed 2-5 to 0-6 at the break.
Armagh banged over seven of the opening eight points at the start of second half to kill off Louth hopes.
Grimley split the posts twice to take his tally to five points and three came from Clarke, who also converted a late penalty.
Armagh are third but just a point behind Louth and new leaders Tipperary.
Orchard forward Rory Grugan scored four points and he was happy with his team's display.
"We were under pressure to keep our promotion hopes alive and it was up to us to put in a performance," he said.
"It was a mad start and these things happen in games but we responded well with a goal and we were in good shape at half-time."
Armagh moved to within a point of top spot with a 3-15 to 0-11 victory over Louth side in Drogheda.