Owen collected Jonas Gutierrez's through ball after Portsmouth midfielder Arnold Mvuemba had carelessly given the ball away to chip over David James for his 29th goal in a black and white shirt.
Strike partner Obafemi Martins doubled Newcastle's lead, before Danny Guthrie completed the scoring two minutes from time after finishing a fine move.
In an open first half which gave evidence that goals were on the horizon, Owen missed an early chance on ten minutes when Martins ran free down the right-hand side but, as his cross found his team-mate, the England striker's deft finish drifted just wide.
Portsmouth then enjoyed a series of opportunities themselves as both Jermain Defoe and Peter Crouch failed to find the target when presented with decent opportunities.
From nothing, Martins stunned the home crowed on 20 minutes as his dipping 30-yard effort beat James at his near post but cannoned away off the face of the woodwork.
Newcastle goalkeeper Shay Given was also called into duty as Niko Kranjcar's mis-hit strike clipped Fabricio Coloccini's left boot and forced the Republic of Ireland international into a low left-hand save.
The second half then belonged to Newcastle as Portsmouth ran out of ideas and were punished by some incisive finishing.
The opening goal was all of their own design as Mvuemba's attempted cross-field pass was intended for Nadir Belhadj but was intercepted by Gutierrez, who released Owen to do the rest.
Five minutes later, Defoe drove an effort just wide for the hosts, but that was as good as it got as Newcastle showed no mercy.
On 77 minutes, Portsmouth lost possession from a throw-in and Jose Enrique nudged the ball into Martins to finish from close range.
The emphatic scoreline was completed when Owen and substitute Shola Ameobi combined to take advantage of the space in behind the Portsmouth defence for Guthrie's right-footed shot to curl into the far corner.