Saido Berahino and Gareth McAuley scored in each half as the Baggies registered only their third win of the Premier League campaign.
Clarke was pleased to see his side seal victory following a turbulent few weeks, with a surprise victory at Old Trafford followed by a credible point against Arsenal, prior to enduring a stalemate at Stoke ahead of last Saturday's loss at Liverpool.
With the wind swirling and rain pouring in the Midlands, West Brom adjusted well to the conditions and while conceding it was not a classic victory, Clarke expressed his delight at the Baggies' performance.
"They were difficult conditions, for both sides, but I thought we did more than enough to deserve the win," he told Sky Sports.
"We started well and got control of the game. We spoke about starting well and early on it looked like it was going to be a long afternoon for Palace.
"The most important thing is that we come away today with three well-earned points."
Clarke was forced into making a change in the 20th minute when full-back Billy Jones limped off and the West Brom boss opted for striker Berahino, with Morgan Amalfitano slotting into the left-back berth.
The switch was vindicated just before half-time as Berahino fired West Brom into the lead with a powerful shot and Clarke hailed the impact of the England U21 forward.
"I could have gone with another defender," he admitted. "But I just felt it was too early in the game to commit to another defender on the field.
"I like to try and be positive with my substitutions. I spoke to Morgan and he assured me he had played right-back before and he did great there.
"We brought Saido off the bench and it's well documented he has done well for us this season.
"He's a good finisher, his first touch wasn't the best, but he's two-footed and as soon as it lands on his left foot, he hits it well and the keeper had no chance."