The 38-year-old Klitschko, who also holds the WBO, IBO and WBA titles, knocked down the 33-year-old twice in the opening round as Pulev initially struggled to keep his taller opponent at a distance.
The Bulgarian, who had won his previous 20 fights, was again floored in the third round when he was sent sprawling by a thundering left hook.
He looked to be finding his way back into the fight, landing a big right that rattled the Ukrainian but another giant left hook finished the job in round five with a dazed Pulev staying down for the count.
“I made my professional debut here 18 years ago and I love this city,” a beaming Klitschko, who has his base in the northern German city, said in a ringside interview.
“It was difficult to get that hook in. I kept trying but he managed to stay away. I tried it a few times and at the end it worked.”
Klitschko has now improved his record to 63 wins out of his 66 fights with 54 knockouts. Pulev is 20-1.
“I feel good,” Pulev said, nursing an ice pack on his quickly swelling right cheek. “I am satisfied with my performance. Wladimir is a good opponent but I think he had a bit of luck.
“Now I want revenge and it will be different result,” said the Bulgarian.