By performing a direct rollover from the 401(k) to the IRA, you avoid 20% mandatory tax withholding on the distribution from the 401(k). If the distribution was instead paid to you and then rolled to the IRA within 60 days, you would have to replace the amount withheld for taxes with money from another source to complete the rollover of the entire amount. Even though you still may need to have some money withheld for taxes or pay estimated taxes to avoid a tax underpayment penalty, you don't want that withholding to come from the 401(k) since the distribution from the 401(k) doesn't qualify for the higher education-expense exception. For your distribution from the IRA, make sure that the gross amount distributed (which includes the amount of any taxes that you choose to have withheld) do not exceed the education expenses for the year.
