A first-half strike from Jaidon Anthony looked like it would be enough to separate the sides in a crucial clash near the bottom of the Premier League, but Sam Surridge's late leveller meant the spoils were shared.
Forest looked lively early on but failed to react after going a goal down shortly before the half-hour mark.
However, fewer than 10 minutes after his introduction from the bench, Surridge came up with an equaliser from close range after good work from Brennan Johnson.
Even during his time as caretaker, O'Neil's record with Bournemouth was not great, as he won just four of his 18 games in charge coming into this one, and things looked perilous after the Cherries lost all six games since returning from the World Cup break.
They also failed to score in five of those six defeats, so O'Neil will have been desperate for a response from his side, especially from his players in the final third.
Forest have been notoriously poor travellers this season though, having scored just two goals in their nine matches on the road.
However, they were the side in the ascendancy during the early stages as Morgan Gibbs-White forced Bournemouth keeper Neto into a fine save inside five minutes.
The visitors thought they took the lead soon after, when Ryan Yates fired home after a cushioned knock-down from Willy Boly.
A VAR intervention cut their celebrations short soon after though, as it was revealed Boly had strayed offside from Gibbs-White's set-piece delivery.
Against the run of play, the hosts then took the lead with their first Premier League goal since before the World Cup break.
Dango Ouattara, making his debut today, swept in a low cross, and Anthony remained composed with an excellent first touch and finish beyond the reach of Wayne Hennessey.
Forest struggled to react to going a goal down and almost fell two goals behind when Kieffer Moore fired narrowly wide just after the hour mark.
It was a quiet second half as a whole, but the visitors looked more lively after the introduction of Surridge with a quarter of an hour remaining.
It would be the 24-year-old who got the important equaliser for Forest, as he was in the right place at the right time to prod home from almost on the goal line after Johnson's square ball across the area.
The final minutes of the game produced no moments of note as the two sides played out a draw, a result which will feel underwhelming for Bournemouth given the position they were in heading into the latter stages.
The Cherries have slipped into the bottom three after West Ham United's win over Everton today and now face the tough test of travelling to an in-form Brighton & Hove Albion side in their next league encounter.
For Forest, it was a point they will be pleased with, but this result extends their record to just one win from 10 away league games this season, and Cooper's side now have a EFL Cup semi-final double-header against Manchester United on the horizon before their next league outing.