The Wee County outfit took control in the early stages with Peter Kirwan and William Woods putting over fine scores from play to lead 0-4 to 0-1 after 11 minutes.
Offaly’s cause was not helped by a couple of dreadful misses from frees by Anton Sullivan before the break, when the board 0-6 to 0-1.
The highlight of that opening period was a brilliant point by Louth midfielder Shane O’Hanlon following a defence-splitting solo run just before half-time.
Colin Kelly’s side looked to be in cruise control when increasing their lead to eight points three minutes after the restart.
Offaly came storming back, however, with substitute Peter Cunningham making a big impact with five points. But further missed chances and some heroic Louth defending saw the Wee County men through.
The winners finished with 14 men, Ruairi Moore picking up a second yellow card at the end.
Scorers for Louth: W Woods, B Rogan (1f) 0-2 each, E O’Connor, S O’Hanlon, R Moore (1f), P Kirwan, B Hamilton, B Berrill 0-1 each.
Scorers for Offaly: P Cunningham 0-5 (3f), D Hogan, A Sullivan, A McDonagh 0-1 each.
OFFALY: G Shiels; C Donoghue, E Rigney, J Kavanagh; S Hannon, J Ledwith, J McFadden; M Brazil, D Kelly; D Hogan, A Sullivan, G Guilfoyle; T Spain, B Allen, S Cullen.
Subs: M young for Cullen (25), P Cunningham for Spain (26), N Bracken for Kavanagh, D Hanlon for Donoghue (both 33), A McDonagh for Hannon (53).
LOUTH: J Flanagan; C Murray, D Campbell, T Hand; M McKeown, P Reilly, A Williams; E O’Connor, S O’Hanlon; R Moore, C Bellew, P Kirwan; B Rogan, W Woods, B Hamilton.
Subs: E Duffy for McKeown (35), B Rerrill for Hamilton (51), E O’Neill for Kirwan (55).
Referee: F Barry (Kildare).