Jason Spice dived over in the final minute to leave the ever-improving Blues one win from the semi-finals.
That late try denied Leicester Tigers a bonus point which could prove crucial for qualification come the final round of pool matches next Friday night.
Cardiff were chasing a fifth win in a row, and a third English scalp in succession after victories over Sale Sharks and Gloucester , and seized the initiative after five minutes through Ben Blair’s penalty.
But despite their dominance, Cardiff fumbled a string of half-chances, as rising Wales stars Andy Powell and Leigh Halfpenny ran riot, with a narrow 6-3 lead at half-time.
But when the passes finally stuck, the try came easy for Jamie Robinson five minutes into the second half.
Jamie Roberts burst onto Nick Robinson’s flat pass, Flood and Dan Hipkiss were caught napping, and the Wales centre delivered a scoring pass to send Robinson under the posts.
Derick Van Hougaard offered a glimmer of hope for Leicester , finalists in the Anglo-Welsh competition for the last two years, with two second-half penalties to narrow the gap to 13-9 on 67 minutes.
But a gutsy defensive effort from the Blues kept Leicester at bay. Leigh Halfpenny and Taufa’au Filise both went close before Blair struck a second penalty seven minutes from time.
Then Halfpenny’s catch, step and pass set up Spice for the late try that suggests the Blues could be genuine cup contenders.
