How does the”automatic revalidation rule” work?

It appears that you may be able to.  The automatic visa revalidation rule is an exception to the general requirement of having a visa in your passport in order to return to valid temporary nonimmigrant status in the United States. The rule does not apply to foreign citizens coming to the United States for the very first time. Rather, it applies to those foreign citizens who have already obtained at least one visa from a US Consulate overseas and have been maintaining that status or another status inside the United States. The automatic visa revalidation rule allows a nonimmigrant to return to the United States without a valid visa in the following situation:

The individual’s currently valid passport contains an expired visa. (If the expired visa is an expired passport, the individual must also have a new valid passport and must present both passports.);
The individual has proof of having maintained nonimmigrant status inside the United States before leaving for the trip. (For example, an F-1 student must present a valid SEVIS I-20 form and I-94 card showing “duration of status”. An H-1B worker must present a valid Form I-797 “Notice of Action” approval notice with unexpired I-94 card, and preferably a recent paycheck.);
The individual has been in Canada or Mexico2 for 30 days or less. During that trip, the individual cannot have traveled to a third country (for example, no traveling from Canada to Iceland back to Canada within the 30 days’ window, or from Mexico to Guatemala to Mexico within the 30 days’ window.);
The individual must still have an approved period of status to come back to. (For example, an F-1 student must still be enrolled in school with time left on the I-20 form and/or still have valid Optional Practical Training time left. An H-1B worker must still have approved time left on the Form I-797 and I-94 to authorize returning to work immediately upon returning to the United States.);
The individual cannot be “inadmissible”, which means cannot be ineligible for a visa for various reasons such as criminal convictions, communicable diseases such as HIV, or past history of “unlawful presence” in the United States; and
The individual cannot be a citizen/national of Cuba, Iran, Iraq, Libya, North Korea, Sudan, and Syria (countries that are identified as sponsors of terrorism by the US Department of State).

NOTE: The automatic visa revalidation rule cannot be used by an individual who during the trip to Canada/Mexico applied for a visa at a US Consulate and who was refused a visa. It is common for citizens of other countries besides Canada and Mexico (for instance, an H-1B worker from India) to want to apply for a visa at one of the US Consulates in Canada or Mexico rather than apply back their country of citizenship. The advantage of getting a visa in Canada or Mexico is that later on during a trip home the lengthy wait for an appointment in some countries (such as India) can be avoided because the individual will already have the visa that they need to return to the USA for the next few years of travel.