West Indies were facing the possibility of being beaten with more than a day to spare in this four-day match at Northampton.
At the start of Saturday's third day, they resumed on 28 for three in their second innings, still 166 adrift of the 341 first innings score posted by the Lions, England's 'A' side.
But Powell (108) shared successive century stands with Darren Bravo (57) and Shivnarine Chanderpaul (77) and by stumps the West Indies had advanced to 377 for eight -- a lead of 183.
West Indies' batting is considered to be the most vulnerable aspect of their game and the way they folded to 147 all out, albeit in seam-friendly conditions, in the first innings did not augur well for Lord's.
Nor did Friday's top-order collapse but Powell and Bravo, whose fifty was his second of the match, both cashed in after they each survived a difficult chance while still in the teens.
Bravo was first to his fifty, when he lofted England spinner Samit Patel down the ground for his ninth four in 76 balls, before he deflected a glance off uncapped seamer Jack Brooks, playing on his Northamptonshire home ground, on to leg stump shortly after lunch.
Opening batsman Powell, in what was only the second first-class hundred of the 22-year-old's career, pressed onto three figures with a 217-ball century including a straight six off Joe Root's off-spin and 13 fours.
The left-hander was, however, out not long afterwards when bowled by a turning delivery from Patel.
Chanderpaul, officially the world's best Test batsman, proved typically obdurate and kept Powell company in a stand lasting 34 overs before the latter was out approaching tea.
He was out in surprising fashion, the left-hander misjudging a ball from seamer Stuart Meaker to be lbw playing no stroke.
England are due to name their squad for the first of a three-Test series on Sunday, with Lions captain James Taylor and Jonny Bairstow, who earlier in this match made a century and a fifty respectively, in contention for a place after all-rounder Ravi Bopara tore a thigh muscle playing for Essex.
