Clarke, who was on target with two goals in the previous home game against Sheffield Wednesday, struck twice in the opening 23 minutes - either side of a spectacular volley from Jody Craddock.
The win got Wolves' season firmly back on track after they had collected just one point from their previous three games as they took to heart the pre-match warning from manager Mick McCarthy that this was a "must-win game."
While Wolves are now emerging as serious contenders for the play-offs, for Southend there appears to be no end to their misery as they gear up for a season-long battle to avoid an instant return to League One.
No-one could doubt their endeavour against Wolves but all they had to show for their efforts was a consolation strike from giant striker Matt Harrold who headed home Mark Gower's 57th-minute left-wing cross.
They have now lost their last three games and failed to win for 12 to leave themselves rooted to the foot of the table.
Despite the best efforts of their highly-rated striker Freddy Eastwood, who hit the bar with a scorching second-half drive, and the hard-working display of Peter Clarke, Southend were ultimately undone by a poor defensive display that cost them dearly against Wolves who left them reeling with three goals in the space of just 13 minutes.
United's normally reliable goalkeeper, Darryl Flahavan, gifted Clarke his first goal and that ultimately signalled the beginning of the end for the Shrimpers.
Ironically, things could have been a lot different had Steve Hammell's second minute free-kick not hit the bar with Wolves goalkeeper Matt Murray beaten.
Wolves fully capitalised on that let-off after 10 minutes when Rob Edwards released Lewis Gobern down the right wing. Flahavan spilled Gobern's cross and Clarke calmly slotted home the loose ball after a neat turn.
All hopes of a Southend revival were effectively extinguished just two minutes later when the United defence allowed Carl Cort space to flick on a Gary Breen free-kick into the path of Craddock who spectacularly volleyed home his first goal in 12 months.
Southend's problems in the air were compounded in the 23rd minute when Rohan Ricketts lifted in a left-wing centre that the unmarked Clarke headed home from close range as Wolves ran in three goals at Molineux for the first time in 15 months.