Ireland resumed day four on 64-0 in their second innings having been forced to follow-on by the visitors, who reduced the hosts to 157-6 to seemingly put them in position for an emphatic victory.
Mohammad Amir, having been troubled by a knee injury on day three, looked back to fitness and form on Monday and did much of the damage with figures of 3-57.
But Amir and the rest of the Pakistan attack were frustrated by the brilliance of O'Brien, who forged a pivotal partnership of 114 with Stuart Thompson (53) and an unbroken one of 48 with Tyrone Kane (8), staying unbeaten on 118 to guide Ireland to 319-7 at the close on an historic day at Malahide.
Ireland therefore lead by 139 going into the final day, with a draw and even a victory still within their grasp after being applauded off the field by Pakistan at stumps following O'Brien's magnificent effort.
Opener Ed Joyce (43) was run out by Faheem Ashraf before Andy Balbirnie went for a duck five balls later as Ireland made a dreadful start to the day.
The prospect of defeat loomed ever larger after Amir dismissed any doubts over his ability to produce pace by sending Niall O'Brien's (18) off and middle stumps careering out of the ground, before then claiming the scalp of captain William Porterfield (32).
O'Brien's arrival at the crease prompted the first signs of Ireland resistance but wickets continued to tumble around him until Thompson joined him in the middle.
Their defiance ensured Ireland would not only avoid an innings defeat but also give their own attack something to bowl at in Pakistan's second innings.
And, though a ripper from Shadab Khan removed Thompson, O'Brien proved immovable, his belligerent strokes keeping the scoreboard ticking before he wrote his name in the history books by sneaking two through point to bring up his hundred.
O'Brien and Kane withstood pressure from Amir, Rahat Ali and Mohammad Abbas late in the day, and Ireland go into the last three sessions with the unexpected dilemma of deciding how long to bat before attempting to bowl Pakistan out to seal a seismic shock win.