The Czech Omega Pharma-Quick Step rider escaped in the final few kilometres to take a solo victory after a 183.km trek from Gravelines – Cassel.
Carlos Betancur (Acqua & Sapone ) was second a further 10 seconds back with Thomas Voeckler (Europcar) winning the sprint for third.
Race leader Jimmy Engoulvent (Saur-Sojasun) endured a tough day and was just over a minute behind Stybar but he still hangs on to the leaders' jersey.
He is now 43 seconds ahead of Sybar on GC with John Degenkolb (Argos) now in third position – 51 seconds behind Engoulvent.
The race's fifth and final stage takes place on Tuesday as the riders travel 176.1km from Bethune to Dunkerque.