It all looked rosy for the Young Lions as they took a 2-0 lead at the Akdeniz University Stadium, Antalya, Turkey.
Harry flicked on James Ward-Prowse's corner for Connor Coady to head home the opener on 41 minutes and then delivered an inch-perfect cross for Luke Williams to double the lead seven minutes into the second half.
The striker was soon denied one-on-one and Iraq hit back via an Ali Faez penalty on 75 minutes before clinching the draw in the fourth minute of added time as Ali Adnan fired home.
Alex Pritchard remained an unused substitute.
England next take on Chile on Wednesday afternoon.