Coventry striker Gary McSheffrey's seventh-minute spot kick was saved by Pompey goalkeeper Simon Eastwood before strikes from Jed Wallace and Patrick Agyemang sealed the points for Whittingham's side.
Whittingham said: "A clean sheet is great and to go and score two goals is better.
"Simon did well to save the penalty and that was the springboard for us.
"There are enough games to go for us to stay up, but we know we have a 10-point deduction coming so it is a big ask."
Eastwood's early penalty save heroics came after Coventry striker Cody McDonald had been tripped by Shaun Cooper.
McSheffrey's misery was compounded on the quarter-hour mark as relegation-haunted Pompey took the lead. Wallace played a clever one-two with Cooper before steering the ball past a despairing Joe Murphy and into the roof of the net from six yards.
Eastwood was Pompey's hero again at the start of the second half as he reacted smartly to keep out Cyrus Christie's well-struck curling shot.
The home keeper was called into action once more in the 54th minute, parrying Aaron Martin's long-range shot before Franck Moussa drilled a rebound effort inches wide.
Coventry improved after half-time and it took another excellent save from Eastwood to tip over Moussa's long-range attempt before Agyemang put the game out of reach 14 minutes from time with an excellent flicked header from Liam Walker's centre.