The centre back came into the side at Norwich on Friday, due to John Egan's injury, and produced an immense performance to earn three points at Carrow Road.
And he followed it up against Aston Villa on Boxing Day to make it two wins from two, much to the delight of stand-in skipper Yennaris.
The former Arsenal man said: “He's been a different class. For such a young man, he plays with such an old head.
“He's so composed on the ball. I'm delighted for him getting his chance. He works his socks off in training.
“He deserves it and he's got a great attitude. I'll keep onto him and keep his head. He's got to keep going now.”
The world is at Mepham's feet and the only danger is he gets carried away but Yennaris and co will be making sure that doesn't happen.
He added: “He's not that type of lad. I'm onto him about doing the right things and keep working on and off the pitch.
“There are plenty of boys doing that. There are experienced heads that can guide them and take them under their wing. I'm delighted for Meps as he's playing really well.”
In the 1992/93 Premier League season, Aston Villa and Norwich finished second and third behind winners Manchester United but now they have both been beaten by Brentford in the past week.
“I'm delighted. I think we can perform at such a high level and we've managed to see two games out this time and we can build on it. It's one game at a time so we can't get ahead of ourselves,” Yennaris added.
“We know the sizes of clubs in this league and we've played two of the bigger clubs and we've held ourselves very well.
“It wasn't the cleanest performance and it was a solid team effort and we got the result in the end.”