Romelu Lukaku scored for Albion in the 50th minute, before Robin van Persie netted for United three minutes later and Javier Hernandez bagged the fifth in the 63rd.
Yet Albion provided an incredible finale as Lukaku and Youssouf Mulumbu both scored in the space of 60 seconds in the 81st minute, before on-loan Chelsea striker Lukaku completed his hat-trick to equalize in the 86th minute.
Ferguson will be succeeded at Old Trafford by Everton manager David Moyes, who saw his team beaten 2-1 at third-placed Chelsea in his farewell after an 11-year reign.
Chelsea midfielder Juan Mata slotted home in the seventh minute, Steven Naismith equalized for Everton seven minutes later, but Fernando Torres struck the winner in the 76th minute.
“It’s emotional because it’s the last time I walk away from the players, but part of the job is you move on,” Moyes said.
Chelsea’s interim manager Rafael Benitez, who masterminded the team’s Europa League final victory over SL Benfica in Amsterdam last week, was also saying goodbye, with Jose Mourinho reportedly lined up to return to west London once he quits Real Madrid.
On a day of emotional farewells, Jamie Carragher captained Liverpool on his 737th and final appearance for the club, a 1-0 win over already-relegated Queens Park Rangers at Anfield.
Carragher hit the post in the second half, but Philippe Coutinho got the only goal, lashing home from long range in the 23rd minute.
Manager-less Manchester City, already guaranteed to finish second, were beaten 3-2 at home by Norwich City.
Stoke City striker Michael Owen made a 16-minute cameo appearance before his retirement in his team’s 1-1 draw at Southampton.
FA Cup winners Wigan Athletic, already relegated, drew 2-2 with Aston Villa, while second-from-bottom Reading lost 4-2 at West Ham United and Fulham won 3-0 at Swansea City.