Despite a rasping start and a try after only two minutes, Gloucester could not build on their early advantage and became bogged down against Saracens' more experienced forward operation and their work at the contact area.
It was Gloucester's second defeat within the space of a week but their form earlier in the competition means they will contest a semi-final later in the season.
By the end Saracens were well worth their advantage because they controlled the majority of the second half as the contest developed into a battle of kicking wits and Gloucester couldn't find a way of springing from deep.
However, they went ahead early when Freddie Burns made a lovely outside break to get behind Saracens' defensive line and was able to off-load towards Henry Trinder and he burst clear to the line.
There was plenty of pace in the Gloucester back-line - Trinder, Burns, Charlie Sharples and Dan Norton all had their moments - and they increased their lead with an 11th minute Tristan Roberts penalty after Sarries were penalised for not releasing the tackled player.
That made it 8-0 and although there was also some good work from prop David Young, Jed Hooper and Andres Pretorious, Saracens absorbed everything Gloucester produced.
And they cut the gap three minutes into the second half with and Alex Goode penalty and then, when Norton tried to run out of defence at the end of the third quarter, Saracens turned the ball over and Goode kicked another penalty to make it 11-6.
Gloucester couldn't hold onto the ball or territory for long enough and with the likes of Dave Seymour, Kris Chesney and Hayden Smith getting through plenty of the tough stuff, Saracens grew into the contest.
With 12 minutes remaining they got the try to take the lead. Replacement Jamie Hearn came to the left following a scrum and put full-back Edd Thrower in for the score. Goode made no mistake with the conversion and Gloucester were 11-13 behind.
Goode then landed a 73rd minute penalty before Gloucester raised themselves for one last crack at the end. Scott Lawson, Hooper and Will Waldron were all involved up front but Gloucester couldn't find a way through and Saracens held on for victory.
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