Substitute Lubo Moravcik came off the bench to produce a magical free-kick strike to give jittery Celtic the victory and a 14-point gap at the top of the Scottish Premier League.
Celtic manager Martin O'Neill gave Moravcik the chance to open the visitors up in the 76th minute when he replaced Paul Lambert, but the home fans were becoming increasingly tense and that was rubbing off on the players.
However, O'Neill's decision to bring on the Slovak proved a master stroke when he produced a moment of brilliance to send the relieved Hoops fans wild in celebration.
Strong brought him down just outside the box and Moravcik himself ran up and curled an inch-perfect shot into the top corner of Andy Goram's net.
CELTIC: Douglas, Valgaeren, Mjallby, Vega, Agathe, Lambert, Lennon, Thompson, Petta, Larsson, Sutton. Subs: Gould, Boyd, Petrov, Moravcik, Crainey.
MOTHERWELL: Goram, Corrigan, Strong, Kemble, McMillan, Hammell, Adams, Leitch, Townsley, Spencer, McCulloch. Subs: Connolly, Nicholas, Elliott, Ramsey, Lasley.
Referee: J Rowbotham (Scotland).