Diarra set Pompey on their way with an excellent goal
Lassana Diarra and Jermain Defoe got the goals that gave Portsmouth victory in their first European match and a healthy advantage for the second leg.
Diarra played a one-two with Defoe and volleyed in to open the scoring.
Three minutes later Guimaraes had a chance to level but Joao Paulo Fajardo blazed a penalty over after Sol Campbell hauled down Felix Roberto.
After the break Defoe missed a penalty, having won it himself, but made amends with a superb volley to seal the win.
It was a deserved success for Pompey and in large part down to boss Harry Redknapp's decision to revert to a 4-4-2 formation.
In came left-back Nadir Belhadj for his first start, and winger John Utaka was included after shaking off a knee problem.
Papa Bouba Diop dropped down to the bench, along with Younes Kaboul, but if any concerns that the big midfielder would be missed were soon dispelled.
Diarra was at his fluid best, keeping Pompey moving forward with a variety of passes and also breaking up the opposition attacks.
After only three minutes he played in Defoe but the striker's touch let him down and the chance went begging.
Defoe was then denied by a fingertip save from Correa Nilson after making space for the shot with an outstanding turn.
But the former Tottenham man's fortune changed when he provided the assist for Diarra, who had beaten three men the wing before passing to his team-mate and then volleying home.
But when Roberto was dragged down as Campbell headed clear, Guimaraes looked set to equalise from the spot.
However, Pompey were handed a reprieve as Fajardo's effort clipped the bar on its way over.
Only four minutes into the second half, it was Portsmouth's turn to try to score from the penalty spot after Defoe had been felled by Guimaraes skipper Joao Moreno.
It proved just as difficult for Defoe as it had been for Fajardo, with Nilson once again producing a fine stop.
Luckily for Defoe he had to reflect on that miss for only 12 minutes.
The excellent Beldhaj produced a inch-perfect cross from the left and Defoe instinctively and precisely volleyed the ball into the corner to make it 2-0.
It now seemed that Portsmouth were in full flow, as the party atmosphere had been since kick off.
Guimaraes had other ideas, and began to push for an away goal that would have given the tie a very different balance.
Roberto went close when very nearly beat David James with a free-kick into the box that evaded all but the keeper's leg.
Pompey were now playing on the break, but on one of their counter-attacks they might have wrapped up the tie had Armand Traore not blasted his shot at Nilson.
However, they had already done enough to put them to make sure their first outing in Europe would be a successful one.
Portsmouth boss Harry Redknapp:
"I don't know if that is enough. It will not be easy out there.
"We scored good goals and played well against a very good technical side. But we saw enough of them to believe they could be really dangerous at home.
"It was a great night for supporters and they have deserved it. They have had to endure the bad times for years."
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