I sold shares of a mutual fund & other stocks in order to put a down payment on a first-time home purchase. Do I still have to pay capital gains tax on those investments even though the $$$ was invested straight into a home?

Yes. If the funds were sold in a taxable account, you will still pay tax on the capital gains. If that money was in a IRA, then it will be taxed at the regular income rate but you will not have to pay the 10% penalty. In this case you can pull out a maximum of $10,000. If it was in a Roth IRA and you have held it for 5 years then you can pull out the principal tax free.