Cassidy, 19, on loan from Wolves, struck 11 minutes from time for the hosts before Robinson slotted home a second just four minutes later - maintaining Tranmere's perfect home league record.
Meanwhile, Coventry are without a league win this season having lost their last three games and are still searching for a permanent successor to former boss Andy Thorn who was sacked at the end of August.
Richard Shaw, in temporary charge alongside Lee Carsley, watched on as his Sky Blues side made much of the early running and hit a post through Carl Baker's second-half header.
Buoyed by that chance Adam Barton lashed a shot goalwards moments later that Owain Fon Williams did well to parry wide.
But Cassidy poked his fourth goal of the season home with the outside of his foot after 79 minutes before Robinson steered Joe Thompson's neat pass in off the post.