The big Aussie pulled off a fabulous penalty save to deny Robbie Fowler deep into the five minutes of stoppage time.
Had Fowler found the net City would have snatched the UEFA cup spot from Boro in what was a winner takes all match.
And in what was an incredible finish, City manager Stuart Pearce even switched goalkeeper David James to a makeshift striker as City looked for a winning goal.
Boro, needing one point to guarantee their European place, preserved their remarkable record of having never lost to City in the Premiership, a sequence now stretching to 12 matches.
The Teessiders had stolen the lead midway through the opening period against the run of play.
Fowler fouled Jimmy Floyd Hasselbaink 30 yards from goal and the Dutch striker picked himself up to fire home an unstoppable free-kick which went in off the underside of the crossbar.
City could not have dreamed of a better start to the second half as they drew level within the opening minute.
Kiki Musampa raced on to a pass from Joey Barton and burst past Ugo Ehiogu into the penalty area before shooting low past Schwarzer.
There was controversy midway through the half when Ray Parlour, booked for a foul on Claudio Reyna, committed another bad tackle on Shaun Wright-Phillips minutes later.
Referee Rob Styles, who had booked six players, should have sent off Parlour who escaped with a warning, to the fury of City players, management and fans.
Pearce caused a sensation with two minutes to go as his side pressed for a winning goal as he brought on reserve keeper Nicky Weaver, enabling James to switch to striker.
Then deep into injury time came the City penalty, which was awarded for a handball by Boro defender Franck Queudrue, but Schwarzer came to his side's rescue and dashed City's hopes.