The 2012 Olympic gold medallist, 25, wore down his opponent with some heavy punching, putting the 37-year-old on the canvas three times in the third.
Joshua said: "Expectations were high and Jason was an awkward opponent."
Later at Newcastle's Metro Radio Arena, Anthony Nelson won the vacant Commonwealth super-flyweight title.
The 29-year-old from South Shields beat 23-year-old Scot Jamie Wilson, who retired on his stool at the end of the sixth round.
Joshua, meanwhile, will next face Kevin Johnson on 30 May after pulling out of a scheduled contest with the American in January because of a back injury.
He said: "I was a bit ring-rusty and was not able to display all I've been doing at the gym."
Elsewhere, Canadian Adonis Stevenson retained his WBC light-heavyweight world title with a unanimous points victory over Sakio Bika in Quebec City.
Stevenson, 37, took his career record to 26-1 with a 115-111, 116-110 and 115-110 win on the scorecards.
Australian Bika's defeat was the 35-year-old's seventh in 42 fights.
Unbeaten English heavyweight Anthony Joshua stopped Jason Gavern in round three to record an 11th successive victory since turning professional.