It was West Ham's first defeat in eight games with Brooking in control and the former England star did not hide his feelings about either player.
Defoe, already booked after a spat with Nyron Nosworthy in first-half injury time, was in trouble again ten minutes from the end when he exchanged words with assistant referee Mark Ives.
The Surrey official attracted the attention of referee Paul Armstrong who brandished a straight red card and the Hammers striker was given an early bath.
Repka's reckless moment came when was adjudged to have fouled Gills youngster Danny Spiller well outside the box.
The Czech defender got into trouble by pulling Spiller up by the shirt and wagging a finger at him, but it was to cost Hammers dearly as Marlon King drove home the free kick to give Gillingham the lead.
It was the first ever League meeting between the two sides and King curled his effort wide of the wall past David James' outstretched left hand, for his third goal in successive home games.
Repka almost gifted Gillingham a second, just managing to drag the ball off the line, but he was involved again for Gillingham's second which completed an unhappy afternoon for the Hammers.
Substitute Trevor Benjamin saw his effort deflect off Repka into the net and despite late West Ham pressure Gillingham held out for one of their best victories in recent times.
Benjamin only completed his move to Upton Park late the previous night and did not arrive at his overnight hotel until 1am.
Gillingham: Jason Brown, Nosworthy, Cox, Hope, Wayne Brown, Hessenthaler, Saunders, Spiller, Shaw, King, Sidibe. Subs: Bossu, Hills, Smith, Benjamin, Perpetuini.
West Ham: James, Repka, Dailly, Pearce, Lee, Etherington, Horlock, Quinn, Alexandersson, Connolly, Defoe. Subs: Ferdinand, Sofiane, Kilgallon, Noble, Bywater.
Referee: P Armstrong (Berkshire).