This appears to be the earliest "topological" proof:
A TOPOLOGICAL PROOF OF THE CONTINUITY OF THE DERIVATIVE OF A FUNCTION OF A COMPLEX VARIABLE BY ROBERT L. PLUNKETT 1958
http://www.ams.org/journals/bull/1959-65-01/S0002-9904-1959-10251-2/S0002-9904-1959-10251-2.pdf
G.T. Whyburn himself (whose research was foundational to the result) gives his own proof, allegedly inspired by Connell and Porcelli:
Developments in topological analysis, 1961 http://matwbn.icm.edu.pl/ksiazki/fm/fm50/fm50125.pdf
