Olly Barkley (right) had earlier kicked two penalties as Gloucester struggled to find any sort of rhythm in front of a small Kingston Park crowd.
Prop Jon Golding had given the Falcons the edge with a converted try, and Gloucester needed to keep an eye on the result of the Wasps v Dragons game, but Fijian Satala came to Gloucester's rescue with that late try, his first for the club.
Wasps won 21-10 in the other pool game, but with three wins out of three, Glaws finished on top to qualify for March's semis. They'll join Northampton, Ospreys and Blues in the two games at Coventry's Ricoh Arena on Saturday Match 28, when they were due to play London irish at home in the Guinness Premiership.
The Newcastle win possibly hides the fact that Glaws are still struggling to overcome the chronic injury list which is hampering their season, and they are also struggling to get the best out of a squad which does have a lot more strength in depth than many rivals.
Winning by a single point at Newcastle is a lot better result on paper than it ever looked out on the pitch and coach Dean Ryan is desperate for his team to find form as a unit.
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