The newspaper took home prizes for Best Use of New Media, for its datablog, and for Digital News Service of the Year, for website guardian.co.uk.
The datablog, which publishes visualisations and raw data, was "head and shoulders above the competition", according to the judges.
The Guardian's experimental local sites in Edinburgh, Leeds and Cardiff, which are to close after a year, were nominated alongside the main site for the Digital News Service prize.
The Independent's new, smaller sister title i won the award for Innovation and Creativity, and was commended in the Newspaper Design of the Year category.
Other digital categories included an inaugural prize for Newspaper App of the Year, which went to the Sunday Times for its iPad app. The Financial Times was highly commended in the category for its own iPad app.
Other prizes included National Newspaper of the Year, which went to the Telegraph for the second year running, and Regional Newspaper of the Year, which went to the Daily Echo, Bournemouth.
The awards, which have been running since 2002, cover 20 categories rewarding excellence in both printed and digital media.
Last year's winners included Sunday Times, which won Weekend Newspaper of the Year, and the Guardian, which won Best Use of Citizen/Community Journalism for its G20 coverage.
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