Yes, report the 1099 MISC income on your 1120S return since it was for your business. BUT, note that you may get a letter from the IRS stating you didn't report it on your personal return. If so, you should be able to respond to the IRS in writing that it was business income and was included on your 1120S return. Plus, you can provide the proof that all the funds reported on the 1099 MISC went directly into your business bank account, so you will want to make sure to keep copies of the paper trail that all the checks received went into your business account and submit copies to the IRS if they do send you a letter.
Also, as noted, a workaround for this scenario to avoid the IRS flag is to also enter the 1099 MISC income on your personal return, plus enter the amount of the income as a business expense so make the effect wash (zero effect) on your personal return. Enter the expense as a Miscellaneous Expense with a description that the income was reported on your 1120S return.
You also will want to submit an updated W-9 form to your vendor and request them to make future payments to your business instead of to you. https://www.irs.gov/pub/irs-pdf/fw9.pdf
[Edited 2/15/18|5:09 pm]
