The midfielder struck after 53 minutes to secure a deserved victory against the game Ryman League outfit.
It was pretty much one-way traffic all night but, like at Fleet on Sunday, the young side failed to capitalise fully on their dominance.
Charlie Lee (pictured left) clipped the post with a 30-yard screamer after 25 minutes but we'd had numerous efforts before home keeper Michael Kalli was forced into action.
His first save of note came from Lee Barnard's drive after 37 minutes and he did even better to deflect Andy Barcham's effort wide with his feet following Emil Hallfredsson's break. Barnard tried once more in injury time but Kalli was up to the test again.
The second half followed a similar pattern. Kalli did well to tip O'Hara's shot wide and both Barcham and Barnard were wide of the mark before the goal finally arrived. Pressure from Barnard and Barcham led to a mistake in the Cheshunt defence, Hallfredsson picked up the loose ball, fed O'Hara and the 18-year-old slotted into the far corner.
Charlie Daniels' 50-yard run set up Jacques Maghoma to poke just wide, Lee lashed over again and Hallfredsson tried to square to Barnard rather than shoot as a second goal looked on the cards.
Substitute Stuart Lewis started and finished a move after 68 minutes but his shot was cleared off the line. That was it for 15 minutes until Cheshunt's substitute keeper Martin Pete denied Hallfredsson and Barcham within a minute with a few minutes remaining.
Spurs XI: Forecast, Riley (Kyriacou, 67), Daniels, Mills, Defendi, Barcham, Lee, O'Hara, Maghoma (Lewis, 60), Barnard, Hallfredsson. Unused subs: Button, Seanla.
Jamie O'Hara scored as our Spurs XI side beat Cheshunt 1-0 in Friday night's friendly at Theobalds Lane.