The West Midlands outfit made the trip to the Amex Stadium sitting bottom of the Premier League table after accumulating just one point from eight games.
When Brighton scored at the end of the first half and with five minutes remaining to go 2-0 ahead, the writing appeared to be on the wall for O'Neil's men.
Instead, they finally earned some good fortune, Rayan Ait-Nouri halving the deficit before Matheus Cunha's deflected effort in the third minute of added-on time secured a share of the spoils.
Cunha's leveller came just seconds after Brighton had failed to make the most of a four-on-one opportunity at the other end, squandering the chance to move into fourth place in the standings.
'I got my tactics wrong'
Like he did for the spirited effort against Manchester City last weekend, O'Neil lined up with a 5-3-2 formation, arguably forced on them due to their limited central-defensive options.
However, O'Neil revealed after witnessing his side's comeback that he had felt that a back four would have been more suited to facing a team like Brighton.
The Englishman told Sky Sports: "I'm a little bit disappointed with myself really that I started with a five. I know we did well with a five against Manchester City and the lads deserved another go at it.
"But I didn't think a five would fit very well against Brighton today but at least we were quick enough to change it at half-time.
"At 85 minutes when Brighton scored their second goal I thought I was going to be stood here answering some more tough questions.
"The players have given an awful lot and if they keep doing that it cannot continue to go against you."
What next for Wolves?
Despite extending their winless run in the Premier League to nine matches, Wolves have now scored in every top-flight fixture during 2024-25 aside from the opening-day defeat at Arsenal.
Wolves have also netted more goals than 10 other teams in the Premier League before the remaining five fixtures of the weekend.
Sitting in 19th position in the standings, Wolves next play host to 18th-placed Crystal Palace, who square off against Tottenham Hotspur on Sunday.