It took them less than five minutes to open a lead when Costa controlled a pass from Cesc Fabregas, surged forward and cut the ball back for the advancing Hazard, who angled his shot into the bottom corner of Fraser Forster's net.
Former Blues midfielder Oriel Romeu equalised in the 24th minute, forcing home from close range.
But Chelsea, boosted by their FA Cup semi-final win over nearest rivals Tottenham Hotspur at the weekend, took the lead again just before halftime when Cahill headed in from a N'Golo Kante punt into the area.
