With showers forecast and his side 530 runs ahead, Australia captain Michael Clarke declared on 132-3 at the start of day four in Adelaide.
However, the weather did not intervene during the first session, which got off to a nightmare start from an English perspective.
Cook was tempted into attacking a short ball that he top-edged to fine-leg, where Brad Harris ran in to take a brilliant catch.
Things got worse for the tourists when fellow opener Michael Carberry departed to leave England on 20-2.
The duo remain unbeaten on 29 and 18 respectively, while England are 65-2 with five sessions of the second Test remaining.