The Hornets beat their Merseyside visitors thanks to strikes from Graeme Armstrong, Louis Storey, James Fairley and Paul Chow.
Armstrong opened the scoring on 17 minutes before his former South Shields team-mate Storey produced a lovely finish to the double the advantage after the break.
Fairley's superb 45-yard effort after the break made it 3-0 while Hebburn goalkeeper Andrew Jennison saved a weak Cairns penalty at the other end.
City of Liverpool's poor day continued when Denson was sent off and Vase legend Chow capped the win with an injury-time fourth for Hebburn.
However, it wasn't such good news for South Shields as their poor away form continued as they lost 2-1 against Hednesford Town in the Evo-Stik Premier.
Lee Mason's second-half strike wasn't enough for the Mariners who trailed 2-0 at the break to two Dan Sweeney goals.
Shields have now lost five times on their travels this season, including their last three games.
They have slipped to seventh in the Premier League table.