Derby were not inclined towards singing in the rain but after four consecutive Premiership defeats a point at least brought relief for Jim Smith's beleaguered side on an inhospitable evening.
After 12 matches without a win, Derby remain bottom of the table, a point behind now-managerless Bradford, who are their next home opponents on Saturday week. West Ham, on top for the middle part of the contest, had half a dozen chances to score but Derby finished the stronger, with Craig Burley going close in the final moments.
Rory Delap had the first crack at goal, although it was a wild one that did not trouble Shaka Hislop. There was much endeavour from the home side, if no discernible pattern.
Derby goalkeeper Mart Poom was clearly reluctant to handle the slippery ball and he was tested three times before half-time and again early in the second half as Michael Carrick and then Frank Lampard delivered shots pitched awkwardly in front of him. Carrick's effort almost squirted under his body and Lampard's, which he fumbled completely, would have spelt danger had it not spun kindly to a team-mate.
Meanwhile, the first hour was completed with Hislop still waiting to be extended. A long-range effort by Seth Johnson at least passed respectably close but a header by Craig Burley was easily dealt with. Another by a diving Simo Valakari, a half-time substitute for skipper Darryl Powell, sailed harmlessly over the top.
Disappointingly, the two players with the individual flair to break the deadlock had been confined to the fringes, Paolo di Canio for once unable to make more than fleeting impressions, Georgi Kinkladze too often isolated on the flanks.
DERBY COUNTY: Poom, C Riggott, Carbonari, Schnoor, Powell (Valakari 45), Delap, Burley, Johnson, Kinkladze, Christie (Burton 81), Martin (Morris 87). Subs Not Used: Higginbotham, Grant. Booked: Martin.
WEST HAM UTD: Hislop, Sinclair, Ferdinand, I Pearce, S Pearce, Lomas, Lampard, Carrick, Suker (Diawara 64), Di Canio, Kanoute (Moncur 75). Subs Not Used: Potts, Keller, Bywater. Booked: Kanoute.
Referee: P Durkin (Dorset).