Keothavong, who will represent Great Britain at the Olympics, broke four times to win the first set but 21-year-old American dug in to take the victory in three sets.
Wildcard Burdette, who had previously only won one singles match in her professional career, went on to secure a 2-6 7-5 6-4 victory.
Burdette's reward is a clash with second seed Marion Bartoli in the next round.
Keothavong is now set to lose her top Briton status to Heather Watson, who began the week just four places behind her in the WTA standings.
Watson had already reached the second round in California, thus accruing enough points to overtake her compatriot when the new rankings are published on Monday.