Striker Rodney Jack fired home his fifth goal of the season as Crewe took advantage of two defensive errors to lift themselves off the bottom of the First Division.
Jack seized on an error from Portsmouth captain Adrian Whitbread to put his side in front from the edge of the penalty area on 34 minutes.
The diminutive hitman had no hesitation in hitting a right-footed volley which flew over goalkeeper Aaron Flahavan before dipping under the crossbar.
And strike partner Paul Tait ensured Crewe were celebrating their first victory in seven games when he added a second on 63 minutes following another defensive blunder, this time from Darren Moore.
Moore, who completed a £650,000 move from Bradford at the start of the week, elected to clear a ball from his own penalty area instead of leaving a pass to Flahavan.
But the giant centre-back made a total hash of his clearance, scuffing the ball straight to Tait who took his time before measuring a shot and curling it inside the right-hand upright.
Crewe striker Colin Little had twice gone close to breaking the deadlock early on in a poor first half in which on-loan Manchester City midfielder Michael Brown had produced Portsmouth's best efforts on goal.
Brown, who trained with his new team-mates for the first time on Friday, was at the centre of Portsmouth's attacking play and had no hesitation in shooting for goal on sight - only to find Crewe goalkeeper Jason Kearton in outstanding form.
Brown thought he had levelled the scores just after the interval when he burst into the penalty area with only Kearton to beat but the goalkeeper stood up and saved his effort comfortably.
Kearton was again at his best to deny substitute Steve Claridge in the 53rd minute when he dived bravely at the veteran striker's feet to block his shot for a corner.
And, after Tait had extended Crewe's advantage, Kearton produced the best save of the match to thwart Lee Bradbury.
Claridge's pass put Bradbury clean through on goal but Kearton raced from his goal to narrow the angle before saving at full stretch to tip his effort wide for a corner.