Inverness maintained their fine form as they moved into joint-third with a hard-fought win over 10-man Kilmarnock.
Andrew Shinnie scored before his brother Graeme saw a penalty saved by Cammy Bell on the stroke of half-time.
Liam Kelly's stunning effort levelled matters 10 minutes into the second half of an entertaining encounter.
But the Highlanders won it when Bell was sent off after felling Draper, Billy McKay converted the resultant spot kick.
Unsurprisingly, both managers kept the same starting line-ups after respective wins over Celtic in the league and Rangers in the League Cup in Glasgow.
Supporters of both sides would have anticipated a rollercoaster ride after last season's two Rugby Park meetings generated 16 goals, with a win apiece.
The visitors almost took an early lead as the Ayrshire sunshine made way for swirling wind and rain when Doran sliced wide.
Caley Thistle were on top as McKay almost took advantage of a poor Nelson clearance but he also shot wide.
Killie took 18 minutes to wake from their slumber as a McKenzie drive stung the palms of Reguero.
But rather than spark the hosts into life, Inverness took the lead when Shinnie forced home after good midfield work by Draper and Tudor-Jones.
A minute later the visitors almost doubled their new found lead after a poor ball across his defence from McKeown allowed McKay in but Bell did enough to force him wide and save with his feet.
Killie began to grown into the game with Rory McKenzie impressive. The 18-year-old was hauled down in the box, it looked like a penalty by referee Euan Norris waved play on.
He then drew a save from Reguero before Inverness were awarded a spot-kick themselves after Andrew Shinnie was barged over by Nelson just before the interval.
Brother Graeme - who converted from the spot at Ibrox in midweek - saw his effort saved by Bell.
An irate Killie boss Kenny Shiels had to be ushered up the tunnel at half-time as he waited for the ref pitch side.
He needn't have worried as Liam Kelly levelled the game 12 minutes into the second half with a terrific goal.
Last week's Celtic Park hero picked the ball up and thumped it passed Reguero into the postage stamp corner from about 30 yards, leaving the Spaniard clutching at thin air.
At the other end, Bell was busy saving from McKay and twice from Andrew Shinnie. He had been playing well but Bell got his marching orders, bringing down Draper.
Lee Johnson was sacrificed with keeper Kyle Letheren brought on. But his first job was to pick the ball out of the net as McKay sent the Welshman the wrong way.
Killie went close near the end through Kelly, the impressive McKenzie and Harkins, but it is Inverness who remain unbeaten since early September with their fourth win in five.