After a good move up the left on 18 minutes, Dan Bowie played in Declan Brown who netted from eight yards to put ’Wood a goal ahead.
Leading 1-0 at half-time, the visitors gained a stranglehold and missed three good scoring chances before the hour mark.
But then a brilliant run from Dillon McLauchlan preceded him shooting home from a tight angle to double ’Wood’s lead.
Ormiston centre forward Anes Subasic shot home from 14 yards to pull one back with 12 minutes left but Thorniewood comfortably saw out the remaining minutes to progress.
“We were playing a team bottom of the league but they didn’t play like it on Saturday,” said Thorniewood secretary Eddie Lynas. “They were a good side.
"They could have been maybe two up in the first 10 minutes but our defence held firm.
"Throniewood tried to play good football as we usually do and basically we wore them down.
"I feel we could have scored more than we did and we came away worthy winners.”
’Wood host Kello Rovers in West of Scotland League Conference B this Saturday, KO 1.30pm.
"We beat Kello 1-0 at their park earlier in the season but it was quite a hard game,” Lynas said.
"Hopefully with our attitude and the way we play, it can see us through.”