Two of those tries came in the final few minutes to set up a grandstand finish after Gloucester led 26-12 going into the final ten minutes.
However, Saracens paid the price really for not having a front line goal kicker as Nils Mordt only landed one from six attempts.
Gloucester's win was based on a strong forward effort. Until they made changes at half time, they were simply too strong in the scrum with the visitors conceding penalty after penalty.
It was also good to see Alex Brown back in playing action as he enjoyed 40 minutes before being replaced at half time.
Brown made an early impact as he charged down an attempted box kick in the away 22 but Gloucester couldn't take advantage despite incessant pressure.
However, Saracens weathered the early storm and had an opportunity to open the scoring having won a penalty at scrum time only for Nils Mordt's attempt to fall well short.
The visitors kept up the pace and were rewarded for opting to kick a penalty to the corner as a well drilled catch and drive produced a try for hooker Scott Spurling.
The Gloucester pack responded well and a powerful scrum was followed by a similarly effective lineout drive leading to a penalty from Ryan Mills.
The scrum in fact was an area where Gloucester were dominating with the Saracens front row frequently popping up and a lively Kingsholm crowd weren't slow to offer their advice to the referee!
The superiority in the scrum soon produced another penalty chance for Mills and the fly half confidently nudged Gloucester into a 6-5 lead with the half hour approaching.
With the platform set up front, the Gloucester backs then clicked into gear. Voyce came into the line and drilled a lovely grubber kick through which gave Ian Clarke the chance to show his pace, win the race to the ball and score behind the posts. Mills converted for a 13-5 lead.
And the grubber very nearly undid the visitors again as half time approached but the ball bounced unkindly on this occasion and Clarke couldn't gather. Mills added a penalty though to make the half time score 16-5.
Gloucester made several changes to their pack at half time but were quickly on the front foot again and Mills added a 46th minute penalty to extend the lead to 19-5.
The game went into a bit of a lull with Saracens probably enjoying slightly the better of things and the catch and drive worked again on 64 minutes with replacement Brett McNamee claiming the score. Mordt's conversion made it 19-12.
A nervy final few minutes looked on the cards for Gloucester but Clarke then pounced upon a Saracens handling error to outpace the cover and sprint home from halfway. Rory Teague added the conversion for 26-12.
Late tries from Spurling and Taylor made in interesting but Gloucester secured possession as time ran out and booted the ball into touch to secure the win.