James Beattie appeared to have grabbed a point for Sheffield United with a sublime lob before Watson smashed home from the spot to cap a remarkable second half which started with a calamitous own goal from Palace defender Mark Hudson.
Hudson was under no pressure in the 48th minute as he attempted to clear a routine Keith Gillespie cross from the right but, to the disbelief of a tense Selhurst Park, he slammed it into the roof of his own net.
However goals from midfielders Tom Soares and Carl Fletcher appeared to have put Taylor back on track for a much-needed victory before Beattie's classy finish made it seven goals in seven games before Watson struck.
Taylor admitted earlier this week that he was "not confidnt" of keeping his job after a poor start to the season and his side reflected that uncertainty in a nervy start against Bryan Robson's Blades.
James Scowcroft was presented with the first good chance of the match after the enterprising Stuart Green played him in but he showed a distinct lack of confidence as he snatched at the shot and fired tamely wide.
Scowcroft's team-mates looked equally bereft of ideas after a run of five games without a win and it was the visitors who began to control possession as the half wore on.
Jon Stead latched on to a delightful through-ball from Gillespie to sting the palms of Palace goalkeeper Julian Speroni from the edge of the area before Michael Tonge rattled in a drive from 20 yards which Speroni had to palm away.
However, the home side looked a constant threat from set-pieces and after Scowcroft was fouled by Gary Naysmith the unmarked Leon Cort wasted his side's best opportunity of the first half.
Green's delivery was immaculate but Cort's finish was dreadful as he headed wide.
At the other end in-form Beattie then headed a teasing Gillespie cross over as the whistle went for half-time and it took just three minutes of the second period for the visitors to take the lead in comical fashion.
Gillespie's corner was cleared back out to the winger, who put in a low cross which looked harmless.
No United player was within five yards of Hudson but the centre-back somehow contrived to slice the ball behind him and in off the underside of Speroni's crossbar.
It was a cruel moment for a manager under pressure but Taylor's side rallied and were level within 12 minutes through Tom Soares after superb work from Dougie Freedman.
The Scot charged down the left, cut inside Leigh Bromby before showing great awareness to delay for a moment when he seemed certain to shoot and instead roll the ball into the path of Soares.
The midfielder took a touch before driving low beyond Paddy Kenny and into the back of the net.
The Eagles were revitalised and stormed into the lead 10 minutes later through Fletcher's deflected effort.
Left-back Tony Craig was the architect and after swapping passes with the influential Freedman swung in a deep cross which Wales international Fletcher met on the volley.
His strike across goal was heading into the far corner but flicked off the outstretched boot of Chris Morgan en route to give Kenny no chance.
But the Blades equalised six minutes later. Leigh Bromby improvised brilliantly to stretch and divert an aimless ball over the Palace defence and the alert Beattie was onto it in a flash.
The former England international took a touch before deftly lobbing over the advancing Speroni.
But the drama was not over and referee Kevin Friend etched his name on proceedings by awarding Palace a penalty in the dying seconds when Morgan was harshly adjudged to have fouled Fletcher.
Watson kept his nerve to fire home and hand his manager a timely reprieve.