However, Adam Matthews burst into the Inter penalty area in the 24th minute and cut the ball back to Stuart Armstrong, who side-footed into the net.
Just two minutes later the Glasgow club were back on level terms with new arrival Armstrong once again in the right place at the right time.
Stefan Johansen scooped a Matthews throw-in into the opposition area and, under pressure from Armstrong, Hugo Campagnaro turned the ball into his own net.
Celtic were very much in the ascendency by that stage, but Roberto Mancini’s side snatched a goal against the run of play after a bad error by Gordon just before half-time.
The Scotland No.1 failed to deal with a long ball upfield from Gary Mendel and gifted Palacio possession. Such was the pace on the through ball the Inter player had no chance of reaching it other than through Gordon’s second blunder of the evening.
The 33-year-old Argentinian must have thought it was his lucky day as he had the simplest of tasks to stroke the ball into the empty Celtic net.
Gary Mackay-Steven, Nir Bitton and substitute Liam Henderson, who had replaced Armstrong, all had good opportunities to equalise in the second half.
But Guidetti finally levelled in the third minute time when he controlled a Henderson chip on his chest and volleyed a left-foot shot into the top corner.