It was a return to form for Simon Johnson’s men, who had failed to find the net in their previous two games against North Greenford and Wallingford & Crowmarsh, losing both.
They took the lead on the half-hour mark when Harris struck home a penalty, and three minutes later, they scored again when Bourne headed past keeper Eddie Cavanagh.
A free-kick led to Josh Tooke halving United’s deficit in the 57th minute, only for Sam Tanner to restore City’s two-goal advantage on the hour mark.
The Cityzens, now playing with great confidence, moved the ball around nicely, and a sweeping move led to Harris netting his second goal of the evening in the 69th minute.
Abingdon, who would have gone above Reading in the standings had they won, kept plugging away and scored a second goal through substitute Helton Biague in the 84th minute.
Wallingford ended the game with 10 men after Isaac Shaw had been dismissed for two yellow cards.
Jenson Mansel pipped Harris for the man-of-the-match award.
On Tuesday, City lost 3-1 at Godalming in the second round of the Southern Combination Cup. Deji Alabi opened the scoring in the 18th minute and Pele Dunn doubled the hosts’ lead in the 58th minute, with George Lawrence adding a third after 66 minutes.
Six minutes later, Henry Paxford netted a consolation goal for the Cityzens.
There were two new faces in Simon Johnson’s team, Matt Hill in goal and Marco Fowler in midfield.
This coming Saturday, City host Rayners Lane and the form book points to a home victory. The visitors have yet to win a league match this season, drawing four and losing seven. Their latest reverse came last Saturday when they lost 2-1 at Holyport, the side immediately above them in the table.
* Woodley United were beaten 2-0 at Brook House, where they had lost on penalties in the Division 1 play-off semi-finals in April.
They suffered an early blow when centre-back and captain Mitch Cooper was forced off with an injury before keeper Morrianne Busse pulled off a fine save to deny the hosts in the 27th minute.
After failing to break down United in the first half, Brook House changed tactics for the second half and substitute Frankie Major opened the scoring with a header from a corner kick.
Woodley came close when their man of the match, Harry Wardle, saw his shot kept out by a flying save from keeper Joe Ringer, but their hopes of an equaliser ended in stoppage time when Deluxe Mwengula broke away and lobbed the ball over Busse.
The win took Brook House to the top of the table, while Woodley are down in 19th position ahead of their game away to fellow strugglers Eagles Land Benfica on Saturday. Next Tuesday (20th), they host Maidenhead Town at Rivermoor.