Anthony Knockaert appeared to have secured a win for the home side when he struck eight minutes from time, but Rooney saved the day with a spot-kick, undoubtedly proving a relief for Koeman, who was seemingly about to see his side lose a fifth league game in six.
The first half was every inch a match between two struggling teams, as neither managed to really take control and the only clear-cut chance fell to Brighton defender Lewis Dunk, who saw his effort deflected wide.
Things did improve slightly in the second period and Everton began to look more dangerous, with Mason Holgate and Nikola Vlasic seeing good opportunities fall their way just after the break.
But there was still an alarming lack of quality in the final third on show from both teams, until Knockaert capitalised on shoddy Everton defending to put Brighton on course for a third successive home win in the league.
There was a twist in the tale, though, as Rooney converted a penalty after bad foul from Bruno and Everton stood firm for a point, wrapping up a manic late show at the Amex Stadium.
The early exchanges showed few signs of what was to follow in the closing stages, with both teams offering very little in attack.
Everton looked marginally more threatening and did eventually have the match's first shot 20 minutes in, but Mat Ryan made a strong save down to his right after Vlasic teed up Idrissa Gueye on the edge of the box.
The hosts finally began to offer a little more from an attacking sense after the half-hour and went close the taking the lead.
A corner was cleared as far as Knockaert on the edge of the box and the Frenchman's subsequent volley struck a defender before landing kindly for Dunk, whose effort was crucially blocked behind by Michael Keane.
Glenn Murray was then presented with a chance moments later, but he stumbled when controlling Knockaert's cross on his chest when he probably should have met the delivery with a header.
Everton looked a little brighter at the start of the second half and nearly went ahead, as Holgate turned Solly March inside out and forced Ryan into an important stop from a tight angle.
And Vlasic saw a better chance go to waste shortly after, slipping at the crucial moment after beating Dunk on the edge of the area.
Things really began to liven up towards the end, however, and Knockaert had appeared to have earned Brighton all three points when he struck in the 82nd minute, stabbing home after Jose Izquierdo's effort was blocked.
But a moment of madness at the other end from Brighton captain Bruno allowed Rooney to score from the spot, with the Spanish defender appearing to elbow Holgate in the face at a free-kick.
Brighton were left hanging on at the end, with Ryan ultimately crucial in ensuring they secured a point, as the goalkeeper made a brilliant double save to deny Kevin Mirallas in stoppage time.
Key Opta stats
- Wayne Rooney has now scored against 36 of the 39 different clubs he’s faced in the Premier League – only Frank Lampard (39), Andrew Cole (38) and Alan Shearer (37) have scored against more in the competition (Jermain Defoe also 36).
- The only sides Rooney has failed to find the net against are Manchester United (5 games), Derby County and Blackpool (2 games each).
- Everton are winless in their last 12 away Premier League games – their longest such run since a run of 13 ending in March 2002.
- Pascal Gross has been directly involved in 83 per cent of Brighton's six Premier League goals this season (2 goals, 3 assists); the highest ratio in the division.
- Meanwhile, Brighton have also scored the highest percentage of goals in the second half of games in the Premier League this season (83 per cent - 5/6).
- Six of the last nine goals Everton have conceded away from home in the Premier League have come in the final 10 minutes of games.