Olofinjana, on a season-long loan from Hull, was only allowed to play on Saturday after Nigel Pearson and Dave Jones struck a deal which also allowed defender Anthony Gerrard to take to the field following his loan switch in the opposite direction last week.
But Pearson must have been regretting the agreement after 20 minutes as Olofinjana rose to power home Whittingham's inswinging free-kick and hand the Bluebirds a slender one-goal advantage they held until nine minutes from time.
That was until Gavin Rae ended the game as a contest with his first of the season to ensure Cardiff have now collected 13 points from 15 in an unbeaten start to their Championship campaign.
Hull provided stern opposition, particularly in the second half, but were left to rue a lack of attacking threat as they extended their unwanted record to 27 away matches without victory.
A sell-out home crowd was left disappointed as hometown hero Craig Bellamy was ruled out of the clash due to injury, along with strike partner Jay Bothroyd and on-loan Manchester United midfielder Danny Drinkwater.
The Tigers handed a debut to centre-back Daniel Ayala after he arrived on an emergency loan from Liverpool.
And the youngster saw plenty of action during the opening exchanges as Cardiff edged proceedings.
But it was Olofinjana who stole the headlines when he broke the deadlock against his employers.
The on-loan Tigers man connected with Whittingham's whipped set-piece to send a bullet header past Matt Duke from close range.
David Marshall turned Richard Garcia's effort around a post at the other end but the visitors were fortunate not to find themselves two down just minutes later as defender Kevin McNaughton struck the woodwork from 20 yards.
A free-flowing encounter then saw Bluebirds full-back Lee Naylor clear Paul McShane's header off his own line midway through the half as both sides threatened to add to the scoreline.
But it was Olofinjana's header which separated the two sides at the break, with the tempo of the encounter having cooled and goalscoring opportunities disappeared ahead of half-time.
Hull started the second period on the front foot but failed to really trouble Marshall, who had recovered from the elbow injury which ruled him out of Scotland's Euro 2012 qualifying double-header.
Whittingham stung the gloves of Duke with a long-range free-kick as Cardiff tried to stir a response to their lacklustre start to the second half.
The visitors' attacking approach was causing problems after the break and, despite Jason Koumas twice firing narrowly wide, the East Yorkshire outfit were posing more of a threat.
But Marshall was still yet to be really tested and Hull were made to pay for their lack of end product when Rae knocked the stuffing out of their fightback, picking up the ball from substitute Aaron Wildig before converting low past Duke.