The opening batsman has just joined the club after moving to the area, having previously played for Sussex outfit Ifield.
Wragg was a consistent run-getter in the Sussex League, twice reaching three figures.
And he showed notice of his talent in hitting 110 for Havant 3rds in a friendly against Hayling 2nds on the island.
Wragg - who had made his debut for the 1sts in a friendly against Portsmouth the previous week - struck 10 fours in his 110-ball 106 as Havant amassed 230-4.
Fellow opener Julian Atkins (29), Ben Turk (24) and Andrew Ransley (31 not out) were also among the runs.
Hayling’s reply began badly when opener Neil Wellington was dismissed by Noel Baiju for a third-ball duck.
His opening partner, Alex Johnson, proved harder to dislodge and was still at the end of the 35 overs unbeaten on 49.
Manon Melville - who has represented Hampshire women at under-17 level - took 2-16 off seven overs as Hayling were restricted to 142-6.
They had been 62-5 before wicket-keeper Zach Gillam (34) helped Johnson add 76 for the sixth wicket.
Joe Williams claimed five cheap wickets and Jacob Harris dominated the batting as Gosport Borough defeated Southampton University in a Sunday friendly.
The opening bowler returned figures of 8-2-25-5 as the students collapsed from 42-1 to 61-6.
They later dipped to 86-9 before the last-wicket pair added 41 - the highest partnership of the innings.
Asked to chase 129 for victory at Privett Park, Gosport were reeling when six of the top seven were dismissed in single figures. And the only man who wasn’t, Jackson Todd, was out for 10.
But Harris, coming in at No 8, whacked 11 fours and two sixes in an unbeaten 62 to take Gosport to a three-wicket success.
Ben Erridge took five wickets in 16 balls as Gosport 2nds thrashed Sussex club Compton in a friendly.
Introduced into the attack as third change, Erridge returned figures of 2.4-1-2-5 as Compton collapsed from 47-4 to 56 all out.
Gosport needed just 10 overs to knock off their target, losing three wickets in doing so.
A Portsmouth XI romped to a nine-wicket friendly victory over Knowle Village.
Steven Hendry (3-27) and Daniel Andrews (3-26) were the chief wicket-takers as Knowle were put in and dismissed for 132 in 29.2 overs at St Helens.
Opening batsmen Charlie Cupples and Alistair Thompson then produced a flurry of boundaries as the hosts won by nine wickets in the 17th over.
Cupples hit 10 fours and a six before retiring on 52, while Thompson flayed 11 boundaries in his unbeaten 49.