Myhill was called into action at the DW Stadium with regular No.1 Ben Foster sidelined after undergoing a minor procedure on a groin injury which has troubled him for some time and he remains a doubt for Saturday's home meeting with Chelsea.
West Brom forged ahead in the 31st minute when James Morrison powered home a header from inside the six-yard box after Chris Brunt's cross from the left, and they doubled their advantage shortly before half-time when Gary Caldwell could only turn Billy Jones' cross-shot into his own net.
Arouna Kone immediately reduced the arrears ahead of the interval, tapping home from point-blank range at the far post following Jean Beausejour's dangerous low cross but it took a wonder-save from Ali Al-Habsi to deny Romelu Lukaku a third after the break.
Clarke said: "Ben is OK. He had a minor procedure. He is back, he is comfortable and we hope he will start training next early next week, that is how minor the procedure was.
"He would be doubtful for the Chelsea game, but beyond that we are hopeful, and I still haven't ruled him out of the Chelsea game yet.
"To speak too much about Ben today would be disrespectful to Boaz. He has waited a long time for his chance. I though his handling was excellent, he made some really good saves. He gave a really assured performance which was great for us and I'm delighted for the boy."
Clarke was relieved to see his side claim their first three-point haul on the road this season, a result which keeps them fifth in the table and level on points with Everton, but he would not get carried away when questioned on their ambitions for the season.
He added: "It was long overdue, our away performances have been as good as our home performances, but is nice to finally get a win away from home, especially at such a difficult place to come. I think this is a really good three points.
"This week we are happy where we are. We just keep working game to game. We have the European champions next at home.
"We will approach that in the same manner we have approached every other game this season. We want to put on a good performance and we want to get another three points. We don't want to look too far ahead."