England were 0-1 after one over and 15-1 after four, but Wright, Alex Hales and Eoin Morgan transformed the innings with a barrage of boundaries.
Jos Buttler and Jonny Bairstow added late muscle to drive England to 196-5.
Afghanistan lost two wickets in the first seven balls and crumbled to 80 all out to go out of the tournament.
Jade Dernbach, Stuart Broad, Graeme Swann and Samit Patel all took two wickets but there was no doubt about the man of the match.
Wright had been in the international wilderness for 15 months before he replaced the out-of-form Ravi Bopara for the two pre-tournament matches against South Africa earlier this month.
An inconsistent performer for England in the past, he has clearly benefited from spells in the Indian Premier League and Aussie Big Bash and come back with a game based around clean, straight hitting.
The Sussex all-rounder smashed six sixes and eight fours in 55 balls as he amassed his highest score in 79 limited-overs matches for England, missing out on a century by one run when he could only collect two from the last ball of the innings.
Wright entered the fray with England in a pickle after Craig Kieswetter played on from the last ball of a maiden first over from Shapoor Zadran.
He began slowly, but his innings took off in the fifth over as he drilled Shapoor for a straight four and a six after Hales had got England going with consecutive boundaries.
Afghanistan showed tremendous spirit in making India work hard for victory in their opening match, but they never came close to troubling a ruthless England side.
Their run chase got off to a woeful start when big-hitting opener Mohammad Shahzad skied the last ball of the first over to mid-off and was swiftly followed back to the pavilion by Shafiqullah, who perished playing a similarly reckless shot.
Superb fielding accounted for the next three wickets as Broad held on to a sharp caught-and-bowled chance to remove captain Nawroz Mangal, Buttler ran out Karim Sadiq and Asghar Stanikzai was brilliantly caught by Bairstow running in from long leg.
Spinners Patel and Swann rattled through the next three batsmen to leave Afghanistan in a hopeless predicament on 26-8, only for an entertaining 44 by Gulbodin Naib to spare them the ignominy of the lowest Twenty20 international total – the 67 scored by Kenya against Ireland in 2008.
Naib’s innings merely delayed the inevitable and when he was the last man out, caught by Morgan off Dernbach, Afghanistan’s World Twenty20 adventure was over.
England, meanwhile, go on to face India on Sunday with both teams already through to the last eight.