Do Nordstrom gift cards work at Nordstrom rack?

Yes.

From nordstrom.com:

"About Our Gift Card & e-Gift Card

Nordstrom Gift Cards and e-Gift Cards do not expire, have no fees and are redeemable at Nordstrom.com, Nordstrom and Nordstrom Rack stores. Simply present your Gift Card to any salesperson at the time of purchase. "