Hammers boss Sam Allardyce has been forced to turn to youth after injuries to centre halves James Tomkins and Winston Reid in recent weeks.
And their replacement, 18-year-old Burke, has impressed everyone with mature performances belying his lack of experience.
Burke was voted Man of the Match on his Premier League debut in the 0-0 draw with London rivals Queens Park Rangers last week and was on top form again to record another clean sheet in the 1-0 victory over Burnley on Saturday.
In both matches he has marshalled two of the most talked about English strikers this season in Charlie Austin and Danny Ings with aplomb. Manager Allardyce has described the youngster's displays as 'absolutely magnificent'.
But they say in football there are no better plaudits than those you receive from fellow players. And the latest graduate from the self-styled Academy of Football's production line has tongues wagging on the terraces and in the dressing room.
Teammate and Hammers midfield star Downing, an England international, has been suitably impressed with how Burke handled himself for the second game running.
"I thought we defended very well," he told West Ham's official website.
"Reece had another good game at the back and has slotted in really well – he’s been a big plus over the last two games.
“We had been conceding late in games and losing points, so that’s two clean sheets and back to winning ways, so hopefully we can finish strong."
Burke is the first Academy player since Jack Collison to feature in consecutive first team matches since the emergence of fellow centre back James Tomkins in 2009.