Ameobi, 27, converted a 68th-minute penalty as the hosts fought back to deny Sunderland a first league double over them in 42 years.
Djibril Cisse had put the visitors ahead with his 10th goal of the season 12 minutes before the break, but a hard-fought contest ended honours even.
Ashley took his seat in the directors' box almost unnoticed, as the players took to the field, knowing that the following 90 minutes could prove pivotal in his club's season.
The visitors had the first half-chance with three minutes gone when Cisse out-jumped Fabricio Coloccini to head down for Kenwyne Jones, who in turn played the ball into the path of Steed Malbranque.
However, French defender Sebastien Bassong got there before his compatriot to clear.
The home side created their first opening after 12 minutes when Ameobi collected Damien Duff's cross and turned smartly before shooting, but Danny Collins was on hand to block.
However, it was Sunderland who almost went ahead with 20 minutes gone when Kieran Richardson's free-kick evaded everyone and hit the post, with Kevin Nolan hacking Jones' follow-up off the line.
Joe Kinnear's men wasted a glorious opportunity to take the lead with 27 minutes gone.
Steven Taylor, playing at right-back, played a one-two with Duff and surged forward before pulling the ball back for Ameobi who skied his first-time right-footed shot high over the bar.
It was Sunderland who took the lead after 32 minutes when Cisse ran on to Dean Whitehead's through-ball. Steve Harper saved his initial effort but Cisse stabbed the rebound home as the home side appealed in vain for an offside decision.
Cisse picked up a knock and made way for former Newcastle forward Michael Chopra in the 55th mnute, with the balance of the game having switched firmly in the hosts' favour.
Sunderland briefly managed to stem the tide, with Richardson trying to take the pace out of the game in the middle of the field, but Newcastle were growing in confidence.
Their big chance arrived with 67 minutes gone when Taylor went to ground under Malbranque's challenge and referee Howard Webb pointed to the spot.
Ameobi blasted the penalty high to Marton Fulop's left as the goalkeeper went the wrong way to level the scores.
The visitors regained some measure of control and might have restored their lead with 17 minutes remaining had Bassong not got a superb block on Jones' shot before Harper denied Andy Reid from the rebound.
Nolan and Ameobi both went close as time ran down, but Chopra should have handed Jones the chance to win it with Coloccini down injured with four minutes remaining, but could not pick him out in front of goal.
Reid sent a left-foot shot inches wide with the final kick of the game, but Newcastle had earned their point.