This PDF has a good list in Table 1.1 of statutes that grant the President wide lattitude in setting Tariffs. Tariffs are not covered under Article I, Section 8 as you quoted, that sectionsentence applies to only internal interstate trade within the boundaries of the United States. The President has much more authority with external trade since that is a form of foreign policy. The more pertinent quote from Article I, Section 8 is a little further down: