Marc Stcherbina, Mark Lewis and Mosese Luveitasau were also try scorers, while Ben Blair kicked 15 points.
Sarries' points came through tries from Ben Johnston and Tomas de Vedia, with Glen Jackson adding the extra 19 from the boot.
The Blues started the game the brighter, with Stcherbina and Shanklin tries sandwiching a Jackson penalty for Saracens.
But the hosts responded with a well-worked try of their own when winger de Vedia crashed over in the corner after good work from his forwards.
Jackson converted from a tight angle and he exchanged penalties with Blair to make it 15-13 to the Blues after 25 minutes.
A further three penalties from Jackson gave Saracens a 7 point lead at the interval, as they went into the break 22-15 up.
In the second half, the Blues strengthened their line-up with recovering skipper Xavier Rush coming on from the bench.
And the Blues' extra class quickly began to show, as tries from Lewis and Shanklin helped the Blues into a 27-22 lead, also giving them a vital bonus point.
A third Blair penalty followed, before Cardiff pulled well clear when Luveitasau intercepted Johnston's pass and cruised over.
Blair's conversion made it 40-22 before Johnston added a late consolation try for Sarries.
After the match, Blues coach Dai Young was full of praise for Shanklin after a superb display from the centre.
"I thought every time he had the ball he looked powerful," he said. "He always looked like he could do something in attack, and in defence he put in a couple of hits.
"It augurs well for Wales in November."
The Blues now stand top of EDF Energy Group B, and a home win against London Irish will see them qualify for the Semi Finals of the competition for the first time.
Saracens (22) 29
Tries: De Vedia, Johnston
Cons: Jackson 2
Pens: Jackson 5
Cardiff Blues (15) 40
Tries: Stcherbina, Shanklin 2, Lewis, Luveitasau
Cons: Blair 3
Pens: Blair 3