Norris was given command of the third-rate HMS "Orford" early in 1702 and served under Admiral Sir George Rooke at the Battle of Cádiz in August 1702 at an early stage of the War of the Spanish Succession. He went on to command the vanguard at the Battle of Malaga in August 1704. He was given command of the first-rate HMS "Britannia", flagship of Admiral Sir Cloudesley Shovell, in 1703 and then served under Admiral the Earl of Peterborough at the capture of Barcelona in October 1705. Following his return to England he was knighted on 5 November 1705.