Callum Wilson netted his 16th goal of the season to give City a first half lead and although Malvind Benning grabbed a leveller just after the break, Delfouneso grabbed the winner for the hosts with just six minutes to go.
Following the 0-0 draw with Shrewsbury on Sunday, City manager Steven Pressley made one change to the starting line-up for the Sky Blue's West Midlands derby at home to Walsall.
Franck Moussa failed a very late fitness test and so Mark Marshall made his first start for Coventry after joining in February.
Carl Baker dropped out of the match day squad as he also failed a late fitness test and so on-loan Nathan Delfouneso came back in after recovering from the groin injury which had kept him out since the Sky Blues' away win at Bristol City in February.
The game began in a tentative fashion with both teams trying to play the ball around in midfield. Coventry's first corner came before the 10th minute after Wilson's effort was pushed away by visiting goalkeeper Richard O'Donnell.
A run from on-loan midfielder Michael Petrasso then resulted in a shot which flew just wide of the post before good work from Marshall on the flank resulted in the start of the Sky Blues turning up the pressure on the Walsall box.
The away side launched a counter attack and forced a terrific save from Murphy after Brandy's shot in the 20th minute was deflected off Webster, the City 'keeper making a superb reflex stop.
The Sky Blues took the lead though after a fine ball from Chuba Akpom to Wilson gave the striker the time and space to place the ball into the back of the net in the 22nd minute. The 22-year- old then ran straight to the touchline to celebrate with physio Dave Hart who had clearly helped in Wilson's recovery from injury.
More decent hold-up play from Akpom lead to more persistence from City after half an hour had elapsed but nothing came from it.
The Sky Blues very nearly took a two-goal lead on the stroke of half time though when a wicked waist-high cross from the right from Marshall almost saw Paul Downing turn the ball into his own net although O'Donnell did fantastically well to tip the ball over the bar from point blank range.
The second half began with attempts for both sides with City midfielder John Fleck attempting an audacious lob from just inside his own half.
Walsall got their equaliser less than ten minutes into half time though. An initial shot from Brandy was parried by Murphy into the path of defender Malvind Benning who had the easy task of tapping home.
With 26 minutes remaining, the visitors created another chance as Benning lifted a freekick into the box but Featherstone blasted high and wide.
Milan Lalkovic won a corner for Walsall which was nudged wide of the goal. His initial shot got a deflection and went behind.
With less than 20 minutes remaining Brandy won a free kick right on the edge of the Sky Blues box which was driven into the box but thankfully for City, the ball was well held by Murphy.
Substitute Blair Adams and Petrasso then linked up well on the left hand side to win a free kick for Coventry but Dan Seabourne couldnt guide his header into the back of the net.
The Sky Blues almost took the lead again after a shot from Adams hit the cross bar from 20 yards. A few moments later, Adams could have scored again but his close range strike wasn't powerful enough to beat O'Donnell.
After the 80 minute mark, sub Ngoo headed a corner over the bar despite being unmarked but as time was running out, sub Delfouneso scored what was a vital winner for the Sky Blues after a brilliant pacey run and pass from Petrasso.
The cut back fell perfectly to the on loan Aston Villa striker whose first touch blasted the ball home from close range with the help of the underside of the crossbar in the 84th minute for a huge three points.
The Sky Blues though needed some heroics from 'keeper Murphy and skipper Seaborne deep into five minutes of added time, Murphy with a double save and Seaborne with a goalline clearance all in quick succession.
An initial shot was kept out brilliantly by Murphy and he did equally well to spread himself and deny the follow up although it was Seaborne on the line who denied Walsall a late equaliser with his clearance out of the goalmouth to protect City's lead and secure their first league win in five games.
Coventry City: Murphy, Webster, Seaborne (c), Willis, Clarke, Fleck, Thomas, Petrasso, Marshall (Adams 65), Akpom, Wilson (Barton 88), Akpom (Delfouneso 62)