Without a manager or a victory on an opponent's ground, Albion came within three minutes of beating Southampton.
The baggies held on until the 87th minute when a shot from Anders Svensson was deflected into his own net by the outstretched foot of defender Paul Robinson.
Two of the Premiership's lowest scorers produced a match of disappointing quality, but plenty of excitement to keep Southampton's biggest crowd of the season occupied.
Darren Kenton brought a save from Russell Hoult early in the match before Southampton went ahead in the 27th minute. Paul Telfer crossed from the right and Svensson made ground the far post before scoring with a stooping header.
There was no time for Southampton to celebrate because less than a minute later West Brom were level with a soft goal.
Zoltan Gera centred from the right and a header from Jonathan Greening was deflected off Earnshaw past goalkeeper Alan Blayney.
Blayney was making his first appearance of the season in place of regular Antti Niemi and he must shoulder some of the blame for the goal.
Earnshaw scored again nine minutes later after Southampton's defence had failed to deal with a shot from Greening and disappointed with his own performance, Blayney spent the interval practising with the club's goalkeeping coach.
Earnshaw should have completed his hat-trick in the 47th minute, but somehow hooked wide from close range when a goal looked to be a formality.
In addition Blayney made two important saves from Greening and Neil Clement as Southampton struggled to get back into the match.
Time was running out when Svensson cut in from the right and his low centre was turned in by Robinson for an equaliser which Southampton only just deserved.
Southampton, badly hit by injuries, were forced to play promising teenager Dexter Blackstock in attack alongside Kevin Phillips, but he made little impression and was booked in the first half for a crude challenge.
Blayney had also keep Southampton in the game in the first half with a 41st minute save to keep out a fierce free-kick from the edge of the area by Gera and West Brom were left to regret a number of missed opportunities at the final whistle.
Stand-in boss Frank Burrows decided to keep former Arsenal striker Nwankwo Kanu as his captain in an effort to make the Nigerian international more involved.
Kanu responded by being spoken to by referee Steve Benett for dissent but made little other contribution until being substituted by Geoff Horsfield 13 minutes from the end.
Man of the Match: Anders Svensson - The Saints midfielder rescued his side with an energetic display that was rewarded with one goal and a major hand in the late equaliser.