An entertaining opening session in Sheffield was the result of both players displaying some nerves, but it was Si who built a slender lead heading into Friday despite being pegged back.
Brecel, who defeated seven-time champion Ronnie O'Sullivan in the quarter-finals, captured the opening frame but Si quickly wrestled control of proceedings by winning the next four to take a 4-1 lead.
Si looked to be relishing his place on the big stage but was given a wake-up call when a missed black in frame six allowed Brecel in to reduce the deficit to 4-2.
World number 10 Brecel backed that up with another frame to close the gap to one and then gave up the chance to level the score with a missed pink.
The error duly was pounced upon by Si, who will be relieved to have possession of a two-frame lead heading into Friday's 10am and 7pm sessions.
In Thursday's other semi-final, which gets underway at 7pm, Mark Allen takes on Mark Selby in what promises to be an intriguing battle.