It came at the expense of a Derby side lacking in conviction in attack and unable to deal in defence with their opponents' impressive speed of thought and movement.
It was a sad way for Derby to celebrate the opening of their new stand which swelled yesterday's attendance to their best of the season. By the end, though, the tears had turned to jeers for Jim Smith's team and it is back to the drawing board for them.
The day had begun unhappily for the Hammers with the news that Andy Impey was to be sold to Leicester City in order to balance the books and Ian Wright's failure to pass a late fitness test would have darkened Redknapp's mood further.
"It does concern me when people want to sell people behind your back," he said. "I should have had the choice of playing Andy Impey today or not playing Andy Impey today. Surely it is up to me as manager and not other people who don't really understand football interfering in my decisions. It's something I'm not prepared to accept."
The loss of Wright, who was not sufficiently recovered from the calf strain picked up playing for England last week, proved John Hartson's gain. The burly Welsh striker, out of favour since his well publicised contretemps with team-mate Eyal Berkovic, returned to partner Paul Kitson in the West Ham attack and it took just six minutes to make his presence felt.
After Rory Delap had shot wide for Derby following a delightful one-two with Paulo Wanchope, Berkovic picked up the ball on the Hammers' right and fed it in towards Kitson near the penalty spot. The former Derby striker failed to get a touch but it ran on perfectly for Hartson who took his chance with aplomb.
Derby's response was somewhat muted and with Berkovic increasingly influential the home side seemed content to play on the break. Another slick move involving Berkovic, Kitson and Hartson nearly provided French winger Marc Keller with an opening but Spencer Prior's long legs came to the rescue and the Derby defender was then denied himself by an excellent save by Shaka Hislop after Prior had headed Dean Sturridge's cross goalwards.
Derby were desperately in need of a fillip and Delap nearly provided it early in the second half, cutting inside Keller into the area. His shot was deflected into the path of Wanchope but the Costa Rican lifted the chance over the bar.
Derby's last chance to equalise fell to Sturridge, who was unlucky to see his back-heel in front of goal find its way straight into Hislop's arms and five minutes later it was all over in the most emphatic fashion.
Ian Pearce galloped down the right and threaded the ball down the line for Berkovic to chase. The little Israeli turned inside and rolled an inviting ball across the edge of the Derby penalty area for Keller who was proving a more than adequate replacement for Impey. His unstoppable right-footed shot went in off the underside of the bar and after that it was all-downhill for Derby.
Goals: Hartson (6) 0-1; Keller (72) 0-2.
Derby County (5-3-2): Poom, Delap, Prior, Carbonari (Harper, 69), Laursen, Dorigo; Bohinen, Baiano (Carsley 12), Powell (Eranio, 86); Sturridge, Wanchope. Substitutes not used: Schnoor, Knight (gk).
West Ham United (3-5-2): Hislop; Pearce, Ferdinand, Ruddock; Sinclair, Lampard, Berkovic, Lomas, Keller (Potts, 86); Hartson, Kitson. Substitutes not used: Moncur, Lazaridis, Margas, Sealey (gk).
Referee: A Wilkie (County Durham).
Bookings: Derby: Laursen, Carsley. West Ham: Ferdinand.
Man of the match: Berkovic.
Football, pages 26-29