Keane, who climbed further up the list of all-time international goalscorers with his 63rd, 64th and 65th goals for his country, tapped in Ireland's first after just six minutes and made it two eight minutes later.
He grabbed his third from the penalty spot on 18 minutes to complete the fastest hat-trick in European qualifying history, beating Marco van Basten's three in the first 23 minutes against Malta 24 years ago.
Gibraltar, who were also beaten 7-0 by Poland in their European qualification debut last month, held Ireland at bay until winger James McClean scored two early second-half goals either side of a comical own goal from goalkeeper Jordan Perez.
Norwich City midfielder Wes Hoolahan added the seventh on 56 minutes as the visitors became utterly overwhelmed and the unfortunate Perez received a standing ovation from the home fans as he was substituted shortly afterwards.
Ireland, who face vastly different opposition in World champions Germany in Gelsenkirchen on Tuesday, were unable to add one more goal that would have equalled their record 8-0 victory over Malta in 1983.
(Reporting by Padraic Halpin; editing by Toby Davis)
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