The Curacao national champion attacked from an elite group of 22 riders inside the final 7km to take the win from Sep Vanmarcke with UnitedHealthcare team-mate Boy van Poppel third, 15 seconds back.
Orica-GreenEDGE's Howard took the golden jersey after Mark Cavendish was distanced on the undulating route.
Former Giro d'Italia champion Ivan Basso invigorated the stage as he attacked after the first climb of the day and formed a breakaway with Bernie Salzberger of Team Raleigh and Bartosz Huzarski of NettApp.
Basso left both of his fellow escapees before the peloton was ripped to shreds on hilly terrain in the Peak District National Park with 40km to go.
Cavendish lost contact with the whittled down peloton and Bradley Wiggins dropped back to assist his team leader but they eventually finished over 10 minutes back.
De Maar attacked on the steep 2.2km category one climb of Gun Hill but it was Britain's Jonathan Tiernan-Locke who crossed the summit first before some regroupment on the 30km run-in to the line in Stoke city centre.
De Maar was on the ground after a number of riders crashed on a right-hand bend but he caught the lead bunch before making his decisive move.
Howard leads Van Poppel by seven seconds on GC with Garmin's Vanmarcke a further 10 seconds back. Team Sky's Christian Knees is 24 seconds behind Howard in fifth with Tiernan-Locke a second further back going into Friday's sixth stage which ends in Caerphilly.