Gareth McAuley scored with their first effort on target, heading in Chris Brunt's 81st minute corner, before substitute Romelu Lukaku fired home an added-time second.
Prior to that goalkeeper Ben Foster had kept out the hosts with a string of saves, including one from Steven Gerrard's penalty after Jonas Olsson was adjudged to have fouled Luis Suarez.
Clarke, returning to Anfield for the first time since leaving in the summer as assistant manager after boss Kenny Dalglish was sacked, felt that was just reward.
"I was pleased with the way we set out from the first minute," he said.
"We were aggressive and we tried to do the right things when we had the ball.
"I thought we played well in the game and deserved to get the three points.
"For me, at this moment in time, Liverpool are playing as well as anyone in the league so to come here and get that result with the performance as well I don't think you can say we were lucky because we weren't.
"When you come to a place like Anfield they have got players who create chances so you know that at some stage your goalkeeper is going to have to make some saves.
"Unfortunately because of the referee he had to make an extra save - I am assured the penalty was harsh but I haven't seen it - but that was important for us as well.
"When he made that save from a penalty that should never have been given it gave us that positive belief and momentum to go and win the game."
Foster was at his best denying Gerrard twice, as well as Jordan Henderson, Daniel Agger, Stewart Downing and Fabio Borini.
Clarke felt his goalkeeper was showing the form worthy of international recognition but respected the player's decision to withdraw from selection a couple of years ago.
"When you see him play tonight I thought there is no reason why he can't play international football except for the most important one - he doesn't want to," he added.
"Ben's made his decision a number of years ago and that's his decision."
The victory was the Baggies' first in the league since Boxing Day and Clarke was pleased for his players, who have had to deal with the backdrop of the Peter Odemwingie issue after the striker drove himself to QPR on deadline day in a failed bid to force through a transfer.
Odemwingie was not in the squad again and Clarke said it was not tough to leave him out.
"It wasn't a difficult decision," said the Scot.
"It wasn't an additional punishment and he was involved, that is why he was there.
"He was in the dressing room, he was delighted for his team-mates and was there to support them and help them.
"It is all part of what being part of a squad about.
"Peter makes his contribution and will make a contribution in the season going forward.
"I am delighted for the players. When things are going well you don't need to praise them because they are getting the results and the plaudits.
"But even in recent weeks when things haven't been going well they have given me everything.
"I am satisfied my players have got some reward for a hell of an effort tonight."