Even after free-scoring Leon Knight twice popped up with equalisers at Peterborough, promotion favourites Brighton failed to give new boss Mark McGhee a winning start.
But at least a dismal three-match losing sequence was halted and McGhee, appointed Brighton's eighth manager in seven years earlier in the week, remained upbeat, saying: "We did well to come back twice and in the end I was satisfied with a point." McGhee added: "There's a long way to go and I took the job because the team is half decent and there is ambition behind the scenes." The game quickly became a battle of the Leons, Posh's McKenzie grabbing his seventh of the season to open the scoring with a glancing header from man-of-the-match Gareth Jelleyman's teasing eighth minute cross.
But Knight levelled on 26 minutes when Nathan Jones got away from Matthew Gill to provide a pinpoint centre.
McKenzie then turned provider as Posh regained the lead within three minutes, setting up Calum Willock, on loan from Fulham, to grab his first League goal with a confidently struck near post effort.
After the break, a lapse in concentration by the home defence was all Division Two's top scorer Knight needed to swivel at the back post and crack in his 13th of the campaign.
Willock looked to have snatched a Posh winner late on but his 20-yard effort crashed against the underside of the bar with Michels Kuipers rooted to the spot, and Brighton also went close when Knight forced Mark Tyler to tip over.
Posh have now equalled their worst ever home League run of nine games without a win and the significance was not lost on manager Barry Fry.
He admitted: "Although the better side for long spells against one of the top teams in the division, we are just conceding too many goals and often chose the wrong option when chances came up at the other end. We are making things very difficult for ourselves."