Dowie headed high over the bar as West Ham applied the early pressure at Upton Park with three successive corners. Barry Venison had taken over as Southampton captain from Matthew Le Tissier, to relieve the off-form player from the added pressures of captaincy and made his presence felt with some telling tackles.
Both teams are too low in the Premiership for comfort, but West Ham, despite having far more of the game, could not carve out a decent opening in the first 15 minutes.
Cottee might have scored after 20 minutes, when following a good run by Michael Hughes, he drove the ball straight at Dave Beasant, but two minutes later Southampton took the lead against the run of play.
Le Tissier had hardly been in the game, but he took an in swinging corner on the left and the ball was deflected into the net by the West Ham midfielder Ian Bishop.
Danny Williamson should have equalised after 24 minutes, but despite being unmarked 10 yards out and with only Beasant to beat, he drove the ball wide.
West Ham won a free-kick on the right of the area and Julian Dicks fired a shot over the bar from Bishop's tap. Southampton's spirits, however, were boosted by their goal and Jim Magilton might have put them two up after 39 minutes when he cut into the box, but shot high and wide.
Then, just before the interval, Southampton were awarded a free-kick on the edge of the box but Le Tissier's lob was safely gathered by Ludek Miklosko, sent off at Goodison Park on Monday night.
West Ham pressed strongly at the start of the second half and Beasant clawed away a dangerous centre from Dicks, then turned a fierce shot from Dowie round the post for a corner.
West Ham were still having the majority of the play, but the Southampton defence seemed capable of holding them out without too much trouble until the double-whammy from Cottee on 80 minutes and Dowie three minutes later.Reuse content