Defoe was at it again as he tested the Newcastle goalkeeper with a fierce left-footed drive, while Crouch was wasteful from 25 yards.
Habib Beye missed arguably the best chance of the half for Newcastle as he headed Guthrie's well-delivered free-kick wide when unmarked.
Despite the chances, neither side could find the breakthrough and not even a moment of individual brilliance from Martins could break the deadlock.
Nicky Butt fed the ball to the Nigerian striker who then unleashed a ferocious curling effort that hit the post with James well beaten.
Not to be outdone, Defoe tried the spectacular as his attempted first-time volley from Nadir Belhadj's cross flew just over, before Given produced a fine reaction save to divert Niko Kranjcar's deflected shot wide.
Adams says Pompey need to be more resilient
Portsmouth wanted a penalty from the resulting corner as they claimed Butt had handled in the area and moments later Defoe looked despairingly at the referee as he went down under a challenge from Sebastien Bassong, but again nothing was given.
Newcastle responded as Jose Enrique tested James at his near post with a fierce left-foot drive, while Defoe squandered yet another chance, dragging his shot wide.
Neither side took their foot off the gas after the interval and it was Newcastle who finally broke the deadlock.
A terrible cross-field ball from Arnold Mvuemba was intercepted by the impressive Gutierrez who fed Owen.
The England striker appeared to have wasted the chance with a poor first touch but, with Sylvain Distin and James diving at his feet, he lifted the ball brilliantly into the back of the net.
Mvuemba was withdrawn shortly afterwards and Portsmouth almost scored an immediate reprieve as Noe Pamarot headed over.
Defoe must have thought it was not to be his day as he again missed the target, slicing wide from 15 yards after skipping brilliantly past Enrique.
We put Pompey to the sword - Kinnear
Newcastle continued to frustrate Portsmouth who were now running out of ideas and it was the visitors who went on to score again.
Enrique found Martins inside the penalty area, and with James committing himself too early, the forward easily stroked home.
There was still time for Guthrie to put the gloss on an impressive Magpies performance and time enough for another James error.
Ameobi's fine work and pull-back down the right allowed Guthrie a shot on goal and James' weak attempt to repel the effort gifted the visitors a third.
Portsmouth manager Tony Adams:
"We're beating ourselves a bit at the moment - we're going to have to stop the mistakes and be a bit more resilient.
"The supporters want to see us going forward and playing entertaining football but if we're conceding goals then it's no good.
"Two areas to work on this week are personnel and tactics."
Newcastle manager Joe Kinnear:
"We played exceptionally well and bossed the game for long periods - the performance had lots of quality.
"Not many teams will put three past Portsmouth down here as it's a tough place to come.
"We are on a decent run now and it gives us confidence for our next game against Tottenham next week."
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