The Saints centre-half played the entire match at the Ricoh Arena, helping the Sky Blues to a result that keeps them fifth in the table, among the play-off positions.
Stephens is now unbeaten in his first two matches for Coventry, following a 1-1 draw away to Port Vale in his first appearance.
City were 3-0 up inside 16 minutes on Saturday, as Chris Stokes volleyed in from a Joe Cole corner in the third minute, before Baily Cargill converted from a Cole free-kick and James Maddison fired in with a low shot.
John Fleck added a fourth before half time, with a strike from distance that found the bottom corner, with Adam Armstrong then netting twice in the space of three second-half minutes to complete the rout.
Fellow Saints centre-back Jordan Turnbull also enjoyed a big win in League 1, as he helped Swindon Town to a 4-1 away success at bottom side Colchester.
After Nicky Ajose opened the scoring in the first half, Turnbull set the forward up for his second of game shortly after the break, playing a quick one-two with Ellis Iandolo down the left and delivering a low ball into the area for the striker to side-foot home.
Just before that, Turnbull had also tested Colchester keeper Elliot Parish with a strike of his own.
Michael Doughty then made it 3-0 when he turned on the edge of the box and found the top corner. Joe Edwards quickly pulled one back for the hosts with a fantastic volley, but Doughty soon restored the three-goal advantage with his second of the match.
The result ended a four-match winless run for the Robins and saw them jump three places to 14th.
Elsewhere in League 1, Ryan Seager helped Crewe extend their unbeaten stretch to five games, with a 1-1 draw at home to high-flying Walsall.
The Railwaymen trailed after 32 minutes, when Tom Bradshaw converted from the penalty spot, following a handball from George Cooper.
Seager, starting his second game for Crewe, came so close to bringing them level shortly afterwards when he met Brad Inman’s left-wing cross with a firm header at the near post, but Walsall keeper Neil Etheridge made an excellent stop to turn the ball round the post.
Crewe did salvage a point, though, when Inman nodded home shortly after the break. The result leaves them 22nd in the table, but in decent form.
Lloyd Isgrove and Sam McQueen both suffered defeats in League 1, for Barnsley and Southend United respectively.
Barnsley had been on a run of seven consecutive victories in the third tier, but that came to an end as they slipped to a 2-1 loss at promotion-chasing Gillingham, leaving them 12th in the standings.
The hosts took a first-half lead when Dominic Samuel broke through and poked home.
Winger Isgrove was substituted just after the hour mark, and although Barnsley levelled through Conor Hourihane’s shot across goal, Gillingham’s Bradley Dack won it when he fired home a loose ball inside the area.
There was also disappointment for Saints forward McQueen, who played 51 minutes as Southend fell to a 1-0 defeat at Scunthorpe, with Paddy Madden’s 11th-minute header enough to separate the teams.
In League 2, Jason McCarthy helped Wycombe Wanderers secure a second successive victory, as they saw off Exeter 1-0 at home.
McCarthy played the entire game at centre-half, helping the Chairboys to a clean sheet, with Stephen McGinn’s brilliant 25-yard effort that found the top corner moving the side up to fourth in the table.