The striker fired low into the corner in the 64th minute to level the score after Nicholas Castillo slotted home a penalty for Chile in the 32nd minute.
Alex Pritchard also made an impact on his first international appearance after coming off the bench just after the hour mark.
Harry had chances before his goal. He was denied by Chile goalkeeper Dario Melo in the 10th minute and just before half-time before dipping a free-kick just wide 10 minutes into the second half.
'Pritch' entered the fray on 62 minutes and after Harry drilled home the equaliser, the tricky forward was denied what looked a certain goal as Melo somehow kept out his close-range header.
The Spurs pair combined for England's final chance in added time as Alex slid in at the far post to meet Harry's low cross, but his effort was blocked.
England now meet Egypt in the final group fixture in Bursa on Saturday, kick-off 7pm UK time. Victory will see them progress to the knockout stage.