Goode, making his first appearance in five weeks, played 56 minutes and emerged unscathed after being dropped on his problematic left shoulder by a tackle from Owen Williams.
The first try arrived in the 36th minute when number eight Robin Copeland pinched the ball at a Saracens lineout 15 metres out and headed for the line, riding a couple of tackles as he crashed over. The preceding half an hour had been uneventful with Nils Mordt and Ceri Sweeney swapping penalties and also missing one apiece, ensuring the Blues led 8-6 at the interval.
Killing the ball at a ruck earned prop Sam Hobbs time in the sin-bin and Mordt punished the infringement with his third penalty.
Substitute Gareth Davies kicked the Blues to within a point with 10 minutes to go, but his fellow replacement Thomas Young was yellow carded in a lively finish.
Saracens landed the killer blow in the closing moments when rampaging centre Duncan Taylor squirted a pass out to wing James Short who crossed, with Mordt converting.