The Scots had been beaten by New Zealand in their tournament opener on Wednesday, when England beat Italy.
An England side showing 10 changes from the Italy match led 2-1 at half-time on Friday after goals from Ellen White and Toni Duggan, which followed an opener from Scotland's Lisa Evans.
Jane Ross pulled Scotland level after 48 minutes and they led five minutes later when Kim Little took on and beat Steph Houghton before firing home.
Rachel Williams cracked a low shot home to make it 3-3 after 73 minutes, and Kelly Smith edged England ahead four minutes later with a close-range finish.
Striker Mitchell, who recently joined German side Essen from Glasgow City, had the final say though, tucking home a 12-yard shot from Little's pass.
England round off their Group A campaign when they take on New Zealand on Monday, and will reach Wednesday's final should they beat the Kiwis.
Scotland cannot reach the final but will be looking to finish their group campaign on a positive note when they tackle Italy on Monday.