The Scottish B international, who signed for Saracens from Bath this year, scored a try and three penalties to cap a man-of-the-match display.
All Gloucester could muster was a bonus point for finishing within seven points of their opponents.
Gloucester's squad was stretched to the limit, with 12 men either injured or on international duty.
And that number increased to 13 with the loss of club captain Jake Boer before the kick-off, the flanker having suffered a groin problem.
Saracens had only five front-line men out but they still struggled to contain the patchwork Cherry and Whites team in the opening exchanges.
Gloucester went ahead after 12 minutes when fly-half Simon Amor slotted a penalty to punish French hooker Raphael Ibanez's wandering hands at a ruck.
It was a pretty dour first half. Kydd kicked a penalty to level the game and added a second to make the half-time score 6-6 after Amor had booted a 25-yard penalty when Saracens were caught offside at a ruck.
Saracens had been closest to scoring a try, centre Kevin Sorrell pulled back for an infringement when chasing a chip through.
But the gloom was lifted a minute into the second half when Saracens went over for the only try.
A long kick to the edge of the pitch on halfway was collected by winger Tevita Vaikona who made ground before passing onto centre Ben Johnston.
He just got inside the Gloucester 22 before being tackled, but managed to release Kydd on his right-hand side and the full-back went over in the corner.
The conversion was missed but Saracens now held the advantage and were on course for a much-needed victory.
Gloucester fought hard, and kept Saracens pinned in their own half for a long period after the interval.
The home defence held firm as the Cherry and Whites returned to their traditional method of keeping the ball tight and letting their famous forwards take the game to the home side.
It nearly paid off for Gloucester when Amor chipped through the home defence inside the 22 only for the ball to stray away from chasing centre Terry Fanolua and home fly-half Mark Bartholomeusz.
The match was getting tough for the home side and it did not help when they gave away another penalty 40 metres out but central, midway through the half.
Amor put boot to ball and reduced the arrears to just two points before Kydd added his third penalty of the afternoon.
The mistake-ridden match failed to spark into any more life other than a few kicks into the corners from the excellent Bartholomeusz.
Both sides ran hard enough but the biggest winners were the defences, whose tackle count must have been immense.
As the clock ticked down Gloucester could not cling onto the final pass or break their way through to get the try that would have put them back into the game.
The victory lifts Saracens seven points clear of Northampton and Harlequins below them in the relegation battle.
For Saracens:Try: KyddPens: Kydd 3
For GloucesterPens: Amor 3