Short answer. Yes. Article 89 lets an employer require overtime specifically where completing or continuing work already started before the eighth hour is necessary to prevent serious obstruction or prejudice to the business. This is one of the recognized emergency-overtime grounds, and you must still be paid the additional compensation the law requires for it.
What the law says
Where the completion or continuation of the work started before the eighth hour is necessary to prevent serious obstruction or prejudice to the business or operations of the employer.
Labor Code, Article 89 — Emergency Overtime Work. Read the full provision →
What the law says
Any employee required to render overtime work under this Article shall be paid the additional compensation required in this Chapter.
Labor Code, Article 89 — Emergency Overtime Work. Read the full provision →
The ground that covers your situation
Article 89 lists specific situations in which an employer may require overtime work, and one of them fits your question directly: where the completion or continuation of the work started before the eighth hour is necessary to prevent serious obstruction or prejudice to the business or operations of the employer. If stopping partway through a task already underway would seriously hurt the business, this ground authorizes finishing it past the eighth hour.
This ground is narrower than it might sound
Read closely, the ground requires two things together: the work must have started before the eighth hour, and finishing or continuing it must be necessary to avoid serious prejudice, not just ordinary inconvenience. It covers completing something already in progress — it does not, by its own wording, authorize starting an unrelated new task after the eighth hour on the theory that leaving it undone would also hurt the business.
The other emergency-overtime grounds around it
This is one of several grounds Article 89 recognizes together — national or local emergency, preventing loss of life or property or danger to public safety from an actual or impending disaster, urgent work needed on machines or equipment to avoid serious loss or damage, and work necessary to prevent loss or damage to perishable goods. Each ground stands on its own; the business-prejudice ground you asked about does not require any of the others to also be present.
You are still entitled to overtime pay
Being required to work under one of these grounds does not mean the work goes unpaid. The article closes with a clear instruction: any employee required to render overtime work under this Article shall be paid the additional compensation required in this Chapter. Being asked to finish the task past eight hours under this provision comes with the same obligation to compensate you for that additional time, on top of your regular pay for the shift already worked.