Some 20 minutes elapsed before either side threatened to open the scoring, as Radoslaw Majewski came within inches of firing Huddersfield ahead, but his 20-yard hit curled just wide.
However, Whittingham soon popped up to show the Pole how it is meant to be done, putting City ahead with a 25-yard thump which nestled into the far corner of the net.
The Terriers should have levelled up soon after, but Jonathan Stead headed narrowly past the post.
It proved a costly miss, as Jones bagged his second of the season by slotting home a John Brayford cross at the second attempt to give the Bluebirds a comfortable lead.
However, Murray Wallace reduced the arrears in timely fashion to give Town a glimmer of hope heading into the second half.