Harris fired home low in the 71st minute after a Sam Hatton corner was only half cleared by Basingstoke.
It was a timely intervention from the ex-QPR centre-back as Dons were struggling to make an impact against a side one division below them in the non league ladder.
Dons goalkeeper Seb Brown had to be at his best to deny the underdogs from opening the scoring in the third minute as he came out well to deny Greg Draper.
And the hosts made light of the gap in class between the two sides in the first-half with Draper again having another excellent first-half opportunity, but Brown easily saved his weak shot.
Though the visitors dominated the possession, Basingstoke had the best chances and only a superb save by Brown denied the hosts.
The hosts worked a short corner and Ross Adams met a Matt Warner cross with a powerful header that Brown was at full stretch to brilliantly tip over.
Dons started to show their class five minutes before the break when Ricky Wellard and Christian Jolley combined to put the returning Andre Blackman through, but his fierce shot was just too high.
Terry Brown's men failed to make an impact after the break and they should have been behind when Stuart Lake had a great chance from 10 yards, but he shot straight at Brown.
The visitors came close to snatching the lead against the run of play when Danny Kedwell lost his marker, but his shot was turned away by Moore.
However, Dons grabbed the lead in the 71st minute when a Sam Hatton corner was only half cleared and Harris fired a low shot into the bottom corner from 12 yards.
Though Basingstoke pressed for the equaliser, Dons held firm to potentially earn a crack at a league side in the first round proper.
AFC Wimbledon: Brown, Hatton, Blackman (Franks), Gregory, Yakubu, Harris, Wellard (Yussuff), S Moore, Kedwell, Jolley, Jackson
http://www.surreyherald.co.uk/surrey-spo....86289-27531799/
I thought I'd start a thread on former Phoenix players and where they are now....