Liam Donnelly missed a second half spot-kick and debutant Callum Lang saw red as Motherwell tasted defeat in Dingwall.
It was a tale of two penalties as Ross Stewart netted for the Staggies in the first-half and Donnelly sent his spot-kick wide for the Steelmen.
And the Steelmen's night got even worse when Lang was sent off three minutes from time for a late challenge on Michael Gardyne.
The Steelmen, who have yet to win a season opener under gaffer Stephen Robinson, rallied after a sluggish first half but couldn't find their way to goal in a frustrating Premiership opener behind closed doors.
Robinson - reportedly on the shortlist for the Bournemouth job - handed debuts to summer signings Ricki Lamie and Nathan McGinley, while Hastie made his second debut in claret and amber following his return on loan from Rangers.
The Fir Park faithful would have been delighted to see David Turnbull make his first start for the Steelmen since May 2019, but the midfielder couldn't make his mark as County's claimed a first home win over 'Well since November 2017.
The Steelmen have looked off the pace in pre-season and it was the Staggies who were full of energy and guile in an impressive first half display.
Chris Long wasted a good opportunity for the visitors early on when he blazed a free-kick over from 20 yards.
The Staggies started the stronger and Trevor Carson, making his first appearance in the Motherwell goal since November 2018, was forced into a terrific instinctive save inside 11 minutes.
Former Motherwell man Lee Erwin's flick on found Stewart at the back post and his thumping strike was turned onto the upright by Carson from point-blank range.
County continued to see a lot of the ball, with Erwin tormenting the visitors down the flanks.
And their pressure paid off midway through the first half when they were awarded a penalty.
Erwin's cross was cleared only as far as Paton and when Gallagher dived in on the Canadian midfielder, referee Nick Walsh showed no hesitation in pointing to the spot and booking the Scotland international.
Stewart stepped up and converted from 12 yards, sending Carson the wrong way with an emphatic finish into the top corner.
Motherwell almost found an instant equaliser when Turnbull's terrific through ball slipped in Chris Long, but his thumping strike smacked off the post and County escaped.
Stephen Robinson changed things up at the break with Lang making his debut from the bench, replacing Mark O'Hara.
And six minutes into the second half Lang got his first sniff at goal when Turnbull's cross from the right picked him out, but he couldn't keep his effort on target.
Sherwin Seedorf replaced Hastie just shy of the hour mark as Robinson looked for a creative spark and his injection of pace down the right almost paid off a few minutes later.
Seedorf's inch-perfect cross put the ball on a plate for Lang unmarked, however his header was straight at Ross Laidlaw.
Motherwell were handed a huge opportunity to get back on level terms from the penalty spot in 73 minutes when Donaldson was punished for a pull on Jordan White, just moments after he climbed off the bench.
Just as it looked like the visitors' luck was going to turn, Donnelly pulled his penalty wide of the target.
Motherwell's night went from bad to worse three minutes from time when Lang was given his marching orders for a late one on Gardyne as he broke forward.
Next up, The Steelmen host newly promoted Dundee United on Saturday and Robinson will be demanding much more from his charges.
Teams
Ross County: Laidlaw, Randall, McKay (Shaw 84), Erwin (Charles-Cook 74), Vigurs, Iacovitti, Tillson (Draper 84), Paton (Gardyne 65), Donaldson, Stewart, Reid.
Motherwell: Carson, Grimshaw, Gallagher, Lamie, McGinley, O’Hara (Lang 46), Donnelly, Turnbull (Watt 83), Polworth, Hastie (Seedorf 59), Long (White 71).
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