Castaignede and Ibanez each scored a try, with a third coming in the guise of a penalty try, and the former French international fly-half kicked two penalties and two conversions for a personal contribution of 15 points.
The Webb Ellis Trophy, which was paraded at the stadium before the game, seemed to provide the right tonic for the home team – despite the cold conditions and damp under foot.
After restraining themselves from celebrating the New Year, ahead of the fixture, the Saracens team had plenty to celebrate afterwards. The four points from the victory saw them close the gap on the teams bunched ahead of them on the standings.
Even though they are still second from bottom on the standings, they are now just two points behind Leeds and Leicester Tigers – the two teams immediately ahead of them.
It was a scrappy first half at Vicarage Road, with most of the action coming from referee Ashley Rowden's pocket. He issued four yellow cards – two to each team – before the break. At one stage, just before half-time, Leeds were reduced to 13 players.
The first score of the match was a Castaignede penalty in the seventh minute.
The first yellow card followed a minute later when Saracens' former Springbok prop Cobus Visagie was sin binned for failing to retreat at a penalty.
Unfortunately for Leeds fly-half Gordon Ross missed the shot at goal. However, in the 12th minute he landed a penalty, which turned out to be Leeds' only score of the day.
In the 19th minute Castaignede made it two from two with the boot and regained the lead for Saracens.
The game then continued in much the same dour fashion as the early stages, with Castaignede having pushed a penalty attempt wide in the 26th minute, before the referee got in on the action again.
In the 35th minute Leeds No.8 Matt Salter was sent to the sin bin for persistent offside. Three minutes later prop forwards Stephen Sparks (Saracens) and Gary Powell (Leeds) were both sent to the sin bin for fighting.
Despite being down to 13 men and also being a man down on Saracens, Leeds pushed hard for the first try of the match. They came close, but Saracens centre Paul Bailey made a try saving tackle in the corner when winger Philip Christophers was racing for the try-line with a clear overlap.
Saracens went into the break with their narrow 6-3 lead still intact.
The first 10 minutes after the break suggested the second half would as dreary as the first, but Saracens coach Rod Kafer made a couple of key substitutions.
In the 42nd minute he brought Robbie Kydd on for Richard Haughton at fullback and three minutes later Ben Skirving replaced Tony Roques on the flank.
Castaignede pushed another penalty attempt wide, but Saracens started to build up a head of steam.
In the 49th minute scrum-half Kyran Bracken had a try denied by the video referee, before he was replaced by Morgan Williams.
But the momentum had clearly swung Saracens' way and in the 53rd minute Saracens were awarded a penalty try from a five-metre scrum. Castaignede added the conversion for a 13-3 lead.
Castaignede pushed a drop goal attempt just wide in the 56th minute, before bursting through to score a great try in the 69th minute. He injured himself in the process of scoring the try and Kydd slotted the conversion while Castaignede was receiving treatment.
With the score at 20-3 it seemed Saracens were in command and they made sure of the win when Ibanez scored after a great passage of play in which Castaignede was instrumental. Castaignede added the conversion to make it 27-3.
In the last few minutes Saracens pushed hard for the bonus-point try, but Leeds held them out.
Castaignede was justly rewarded with the man-of-the-match award.
For Saracens:Tries: Castaignede, Ibanez, penalty tryCons: Castaignede 2, Kydd Pens: Castaignede 2
For Leeds Tykes:Pen: Ross