St Johnstone had enjoyed the better of the opening half hour with Alan Maybury hitting the post and Andy Jackson seeing a shot cleared off the line, but Chris Innes headed the visitors in front in the 36th minute.
Caley Thistle never looked in danger after Doran struck in the 57th minute and Richie Foran soon added a third as the Highlanders moved away from Hibernian.
Saints have now lost five games in succession without scoring and, although they endured some bad luck in front of goal in the opening half, they showed a distinct lack of belief when trying to get back into the game.
The defeat added to the gloom following the Scottish Cup semi-final defeat by Motherwell by the same scoreline, for which goalkeeper Peter Enckelman was the major casualty as St Johnstone made six changes.
Most of them were necessary though with centre-backs Michael Duberry and Steven Anderson suspended and both Collin Samuel and Jody Morris injured.
Inverness made three enforced changes with Innes, Grant Munro and Shane Sutherland coming in for suspended pair Stuart Duff and Ross Tokely plus Jonny Hayes, who has undergone ankle surgery.
Jackson started up front alongside Stevie May for Saints and took just 60 seconds to get a good effort on target from the edge of the box but Ryan Esson got down well to push the ball wide.
Murray Davidson soon threatened for the hosts with a deflected strike from 20 yards that went just wide.
The home side failed to make the most of several set-pieces and Inverness had a half chance when Foran threw himself at Doran's cross but could not turn it on target.
Maybury came very close with a powerful first-time volley from 25 yards which bounced off the inside of the post but Inverness threatened after Graham Gartland was booked for pulling back Foran as the Irishman broke.
Adam Rooney just failed to connect from close range after Innes headed on Doran's long free-kick and Graeme Smith then saved Chris Hogg's header.
The hosts came closer following Danny Grainger's deep corner. Gartland headed the ball back and Jackson hooked it past Esson but Foran cleared off the line.
However, they fell behind when Innes ran on to Sutherland's cross following a half-cleared corner before heading unchallenged into the roof of the net from 12 yards.
Chris Millar curled over from a tight angle and Saints should have levelled before the break when Davidson flicked a long ball past the visiting defence before running clear, but the midfielder slipped the ball wide with only Esson to beat.
Esson saved from Jackson, Jordan Robertson - who was on for May - and Liam Craig within five minutes of the restart but Saints quickly lost their momentum and Doran scored a brilliant second.
Maybury failed to control a long ball to give the Irish winger the chance to run at him and curl the ball into the far top corner from just inside the box.
Inverness comfortably defended their lead, which Foran extended in the 70th minute when he collected Sutherland's header just inside the box and slid the ball past Smith from 14 yards despite having defenders in his way.
St Johnstone have scored just 18 goals in the SPL this season and they looked devoid of confidence as they sought a way back into the game, although Jackson curled just wide from 18 yards.
Rooney could have made the scoreline even more emphatic when he shot over from a decent position.