Sharks were 4-3 up at the halfway stage. That was the signal for Coventry to come to life, goals by Rhianne Oscroft (2), Amy Berry (2), Sancha Tonks and Maisy Clapperton quickly building a 9-4 lead.
Sheffield threatened near the end, cutting Coventry's advantage to a slender 10-9. But the Midlanders had the final say as Pia Tonks netted twice within 22 seconds.
City of Manchester began the defence of their title in style, thumping Hucknall 23-5. Izzy Howe scored five and Rosie Huck four.
In women's Division 2, late goals by Charlotte Hopwood - her fourth of the game - and Holly Rooney clinched Liverpool Liver Birds' 13-11 win against City of Bristol.
Watford beat Cheltenham 8-7 in Division 3 while Penguin Emperors' 12-2 defeat of Liverpool Water Beatles featured a five-goal haul for Cate du Toit.
Photo (Trevor Hyde): Liverpool Water Beatles goalie Rachel Thompson saves a shot from Penguin's Rachel Bull.