If my employer just discovered that my pay rate has been incorrect for about 2 1/2 years, am I obligated to pay even though it was their error?

No, you are not obligated to pay them. They may have paid you more than they "should" have under their internal guidelines or rules, but they did so due to their own error, without you doing anything to cause or prompt it, and evidently without you knowing that you were receiving more than you should have. When you are totally innocent of wrongdoing or (see below) contractual violations, they are liable or responsible for what they pay you, and if they paid you more than they could or should have, need to absorb the cost. 
One possible exception: if you are in a union and the union contract clearly sets out what you should have been paid at your level, for your job, with your qualifications, and you had a copy of that pay schedule, then since you were a party to a contract setting your pay, they could enforce the contract against you and get the overpayment back, the same way that if a plumber contracted to fix your bathroom for $1,500 but you accidentally paid $2,000, you could hold him to the contract and recover $500. But this requires that your pay have been contractually set, in or an attachment to a contract or union agreement which you had access to or a copy of. Only if your pay was actually part of a contract can they hold it to you.
Of course, going forward, subject only to any contractual limitations or requirements for your pay, they could elect to reduce your pay to recoup their "overpayment"--i.e. they can't retroactively get it back from you, but if they have the discretion to set your pay, could use that discretion to reduce what you will get in the future.