A businessman and long-standing St Brelade resident, Mr Jackson received 1,466 of the 2,083 votes cast in the parish - easily beating ex-Jersey Democratic Alliance candidate Mr Pallett, who gained 615 votes.
Mr Jackson told his large crowd of supporters gathered in the parish hall that he was speechless at having been elected.
He vowed to work hard to fulfil their wishes for St Brelade.
Mr Pallett, who is standing in the Deputies election in St Brelade No 2 district on 23 November, declined to comment to the JEP, although his defeat means that in five attempts not a single party or former party member has been elected to office in any election this year.
Speaking to the large crowd gathered in the parish hall for the count last night, he said that he wished Mr Jackson every success.
'People have made clear their choice,' he said, 'and whenever Mr Jackson wants my support, he's got it.'