They were in control for most of the contest on the sunny south coast, although had to remain patient against stubborn opposition.
But the result never looked in doubt once John Marquis had angled home an opener early in the second half.
And Marcus Harness then added the second goal the Blues’ dominance deserved to make sure there would be no way back for the Railwaymen.
Danny Cowley made four changes from the side that were narrowly beaten at Millwall in the Carabao Cup earlier in the week.
Gavin Bazunu was handed his debut between the sticks, while Kieron Freeman, Lee Brown and Harness all returned.
Alex Bass, Connor Ogilvie and Gassan Ahadme dropped to the bench, with Callum Johnson missing through suspension.
A minute’s applause was held before kick-off to remember all those Pompey fans – as well as former players and managers – who have passed away in the past 17 months since fans were allowed inside the ground in significant numbers.
Pompey controlled possession from the first whistle and set about trying to find a route through the opposition defence.
Ronan Curtis nodded over an early cross from Shaun Williams, then sent a long-range effort past the post.
And when Williams then sent a corner into the box, Clark Robertson appeared to have his shirt tugged, only for referee Will Finnie to wave away his appeals.
The deadlock was almost broken midway through the first half, when Brown cut the ball back for Harness.
But he was brilliantly denied by Will Jaaskelainen from point-blank range and Ryan Tunnicliffe then nodded over.
Crewe were not causing too many problems, although Mike Mandron’s header cleared the crossbar from a recycled corner.
And Pompey finished the half with a flourish, as Curtis’ clean strike had to be tipped over by Jaaskelainen.
A teasing stoppage-time cross from Harness was then agonisingly out of reach for both Marquis and Curtis.
Crewe Alexandra 0
A goal looked like it might be coming as the interval approached – and it finally arrived within three minutes of the restart.
Tunnicliffe drove forward with purpose before releasing MARQUIS, who angled in a shot that clipped the inside of the post and nestled in the net.
They seemed to have the initiative and set about trying to find another goal to give the Fratton faithful even more reason to cheer.
But the Blues were almost undone from a corner, with Freeman not able to clear and an almighty scramble ensuing before Callum Ainley eventually dragged a shot wide.
Normal service soon resumed, though, and when the hosts were gifted possession, Marquis collected a cross from Curtis and was not quite able to pick out Reeco Hackett-Fairchild.
The Fratton faithful through their side had gone further ahead on the hour mark after Brown had done well to win a corner.
Williams’ delivery was flicked on by Hackett-Fairchild for Marquis to turn home at the back post, but the flag was raised for offside.
However, a second goal did arrive on 64 minutes after Curtis had switched the ball across the field to Tunnicliffe.
He then found HARNESS and the winger managed to squeeze a shot past defender and keeper from a tight angle.
Cowley soon handed a debut to Joe Morrell in place of Williams, with both players afforded a standing ovation from the crowd.
Two more substitutions soon followed for the home side, as Hackett-Fairchild and Marquis made way for Michael Jacobs and George Hirst respectively.
Pompey remained on the attack as the seconds ticked down and Curtis’ cleanly struck effort from the edge of the box rose inches over the bar.
And they kept pushing for more goals right up until the final whistle, as an impressive start to the season continued.
Pompey (4-2-3-1): Bazunu; Freeman, Raggett, Robertson (c), Brown; Tunnicliffe, Williams (Morrell 74); Harness, Hackett-Fairchild (Jacobs 79), Curtis; Marquis (Hirst 82)
Goals: Marquis 48, Harness 64
Subs not used: Bass, Ogilvie, Gassan, Harrison
Crewe (4-4-2): Jaaskelainen; Ramsay, Daniels, Offord, Adebisi; Lundstram, MacDonald (Finney 65), Murphy (c), Ainley; Mandron (Porter 88), Dale (Long 41)
Subs not used: Richards, Thomas, Johnson, McFadzean
Referee: Will Finnie
Attendance: 11,470 (306 away fans)