The second tier club have just four points from three games - one of which was abandoned - after having 10 points deducted for fielding an ineligible player.
Skipper Dan Harris (72) and Tom South (64) put on 143 for the first Alton wicket, and Portsmouth’s day did not significantly improve thereafter.
The stand was finally broken when Harrison Webb - the sixth bowler used - had Harris caught by Will Smitherman.
That sparked a run of three wickets for as many runs with No 3 Abhay Gonella lasting just three balls before falling to Webb and South dismissed by Reuben McArdle.
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Michael Heffernan became Webb’s third victim at 171 but Scott Myers (53 off 59 balls) and teenager Jude Wright (46 not out off 37 balls) added 79 for the fifth wicket as Alton closed on a daunting 261-5.
Webb (3-48) was the most successful bowler while opening pair Joseph Kooner-Evans and McArdle conceded 106 runs off their 14 overs.
Ben Duggan (42) and Thomas Wallis (25) gave Portsmouth an 86-run start in reply before the latter was trapped leg before by South.
But a promising 93-1 quickly became 104-6 as Duggan, captain James Christian (3), Jack Marston - a first ball duck, giving Jack Myers two wickets in two balls - Will Smitherman (5) and Kooner-Evans (1) were all dismissed.
No 9 McArdle (13) was the next top scorer after the opening pair as Portsmouth were all out for 149 with over eight overs still to go.
The margin of victory would have been even greater had Alton’s bowlers not sent down 23 wides as part of a 29-run extras total.
Xavier Bochereau, the last of Alton’s six bowlers to turn his arm over, cleared up the tail to end with 4-35 off 5.5 overs.
Tailender Richard Walker played the key innings as Portsmouth 2nds defeated their Havant counterparts in a tense Hampshire Districts League encounter.
Portsmouth won by just six runs at St Helens in the County G fixture thanks to three wickets each from Fahad Ahmed, Ethan Randall and Paul Hungerford.
Havant, asked to chase 174 for victory, were all out for 167.
But Walker - Portsmouth’s wicket-keeper - had earlier changed the complexion of the match after walking out to the middle at No 8.
He promptly hit six fours in his unbeaten 49 and shared a key stand with No 10 Randall (21 not out).
Randall ended as his side’s joint top second highest scorer, alongside skipper and opener Jordan Palmer-Goddard.
Captain Pete Hayward (3-24) dismissed both openers - Hemanshu Hirani (13) was the other - and No 4 Henry Woolfe (0), while Graham Burns took 3-13 off eight overs as Portsmouth totalled 173-8 off their 40 overs.
In reply, Havant lost wickets at regular intervals after opener Simon Loat was bowled by Woolfe for four.
Ben Turk (23) was the top scorer among recognised batsmen before he was trapped leg before by Ahmed, who also dismissed Ollie Perkins (0) and Michael Cripps (6).
Randell accounted for Alex Whitfield (13), Oliver Jones (14) and Steve Matthews (6) before Hungerford dismissed Burns (7) and Hayward (11).
No 10 Warren Turner, though, threatened to give Havant an unlikely success by top scoring with 37 in a last-wicket stand with teenager Dan Aitken (13 not out).
That was only ended when Hungerford bowled Turner to give Portsmouth victory.