The Irishman could have perhaps done better for Anthony Martial's second.
With 18 minutes left, the Red Devils threatened to spoil the Irons' farewell to the Boleyn Ground when Anthony Martial deceived the Irish keeper by squeezing a shot inside the near post for his second of the game, having cancelled out Diafra Sakho's 10th-minute opener earlier.
Fortunately for Randolph, Michail Antonio equalised four minutes later, before Winston Reid headed home a dramatic winner shortly after as Slaven Bilic's side flipped the contest on its head to snatch the three points and end their 112-year association with Upton Park on a high - a massive one.
But Brooking was left slightly unimpressed with the 28-year-old, whom he claims should have done more to prevent Martial's and United's second of the night, telling BBC Sport: "Randolph should have been covering the near post. For me a goalkeeping error. A soft goal but a really good counter attack."More importanty, the victory saw West Ham move back into sixth place as Europa League football at the Olympic Stadium looks on the cards next season. Victory at Stoke City on the final day would guarantee that luxury.