Having already seen off China Open winner Mark Williams, Tom Ford and Joe Perry on his way to the final, the world number 27 from Bristol added Robertson to his collection of scalps.
The title was Trump's second tournament success, following his Champions League victory in 2009.
Australian Robertson, victorious at the Crucible at the beginning of the month, took some consolation from defeat with a share of the highest break prize - along with Stuart Bingham - after an earlier 147.
British Open
Allen edges out Trump in nervy encounter to set up Selby quarter-final
Judd Trump 6-4 Neil Robertson
Semi final
Joe Perry 2-5 Judd Trump
Neil Robertson 5-3 Mark King
Quarter finals
Ryan Day 2-4 Joe Perry
Tom Ford 1-4 Judd Trump
Shaun Murphy 3-4 Mark King
Peter Ebdon 2-4 Neil Robertson
Last 16
Ryan Day 3 - 2 Dave Harold
Ricky Walden 0 - 3 Joe Perry
Graeme Dott 0 - 3 Tom Ford
Judd Trump 3 - 2 Mark Williams
Shaun Murphy 3 - 2 Dominic Dale
Matthew Selt 2 - 3 Mark King
Peter Ebdon 3 - 1 Barry Hawkins
Neil Robertson 3 - 1 Stuart Bingham
British Open
Selby makes fourth maximum break of his career in commanding victory over Lisowski
British Open
Trump powers past Xu to reach last 16 but Yan knocked out of British Open