Martin Clarke led the way for Down with five points as they got the better of a determined Offaly side in Tullamore to book their place in Round 4 of the All-Ireland GAA football qualifiers.
Ken Casey's second-minute goal helped Tom Cribbin's charges build a 1-06 to 0-06 half-time lead, before Aidan Carr netted for Down, three minutes after the restart.
Offaly battled back with the sides tied at 1-08 apiece at the end of the third quarter, however Down finished strongly to progress in championship 2010.
The Mourne men had to dig deep to record this hard-fought win at O'Connor Park as Offaly, inspired by Casey's early strike, led for 38 minutes.
18 points separated the sides when they last met in Championship action, back in 2008, and Offaly, obviously to avoid a repeat of that defeat, began brightly.
Casey lit the touchpaper for the Faithfuls, bagging 1-01 inside the opening five minutes as Offaly got an early grip on midfield.
Ciaran McManus booted the ball into Niall McNamee who whipped it out of sky to leave a Down defender in his wake and feed Casey for a crisply-struck finish to the net.
Casey added a point three minutes later, after a tremendous intercept by Ross Brady, with Offaly oozing early confidence.
John Clarke opened Down's account in the sixth minute, and centre-forward Mark Poland followed up by slotting over a quick-fire score to cut the deficit to two points.
McNamee and McManus restored Offaly's lead to four, but Martin Clarke took centre stage with two excellent frees from long range to show Down's ability from placed balls.
It was nip and tuck up to half-time as Anton Sullivan and defender Ross Brady kept Offaly ahead, and a '45' from Clarke saw Down end the opening 35 minutes in good stead.
Three points adrift, Down showed great attacking form on the resumption and were well rewarded for their play.
James McCartan's charges began to force the issue in centre-field, with Ambrose Rogers impressive. Poland fired over his second point with just 45 seconds played in the second half, before Aidan Carr netted Down's goal in the 38th minute.
It was a high quality score which would have made his father, the former Down boss Ross Carr, proud. Collecting a pass from Poland, Carr sent a thunderbolt of a shot to the back of the Offaly net, giving goalkeeper Alan Mulhall little chance.
Carr's goal moved Down in the lead for the first time, and Clarke's fourth point made it 1-08 to 1-06 in the 40th minute.
Following the introduction of John Coughlan in midfield, Offaly got back on track but misfired on two occasions before John Reynolds eventually opened their second half account in the 48th minute.
This was the start of a good patch for the home side who put together back-to-back scores, with McManus tying the game for the first time in the 50th minute - 1-08 apiece.
Scores from substitute Daniel Hughes and Martin Clarke nudged Down two points clear with 15 minutes remaining, but Offaly showed no signs of wilting.
With ten minutes left on the clock, Niall McNamee tried to put McManus through for a score from the tightest of angles, 21 metres from goal, but the roaming Benny Coulter made a superb block to launch another attack for the visitors.
Down had better luck in the scoring stakes during the second half, with a first from play for Poland opening up a three-point gap between the sides for the first time.
Offaly tried hard from defence to attack in the closing minutes, although there were some bad misses for McManus and Reynolds late on.
Down had a late Poland free ruled wide by the referee, despite the umpire raising the white flag, but this mattered little as they held out for a two-point victory.
Scorers: Offaly: K Casey 1-01, R Brady (0-02f), B Connor, C McManus (0-01f) 0-02 each, A Sullivan, J Reynolds, N McNamee 0-01 each
Down: M Clarke 0-05 (0-04f, 0-01 '45'), A Carr 1-00, M Poland 0-03 (0-02f), J Clarke 0-02, B Coulter, D Hughes 0-01 each
OFFALY: A Mulhall; B Darby, S Brady, S Pender; N Darby, R Brady, P McConway; R Dalton, B Connor; G Guilfoyle, C McManus; A Sullivan; K Casey, J Reynolds, N McNamee.
Subs used: S Ryan for McConway (31 mins), J Coughlan for Dalton (42), A McNamee for McManus (67).
DOWN: B McVeigh; D Rafferty, D Gordon, D O'Hagan; D Rooney, J Colgan, C Garvey; A Rogers, K King; A Carr, M Poland, P McComiskey; M Clarke, B Coulter, J Clarke.
Subs used: D Hughes for Carr (46 mins), K McKernan for Colgan (50), R Sexton for McComiskey (55), R Murtagh for J Clarke (63).
Referee: Marty Duffy (Sligo)