Neil Lennon's Bhoys fell behind to the Staggies after just three minutes of their Sky Live encounter, but Anthony Stokes levelled just before the half-hour mark and then netted a winner towards the death (87).
Motherwell had to rely on a late show at Easter Road, too, with new loan signing, Estonian Henri Anier, coming off the bench to fire an 83rd-minute strike past Hibs custodian Ben Williams and earn the Steelmen a 1-0 triumph.
Sky Sports' punditry team - which included former Hibernian midfielder and current Northern Ireland manager Michael O'Neill - watched the action unfurl north of the border.
So read below for their take on whether Celtic's Stokes can fill the boots of the departed Gary Hooper, where Ross County should be looking to finish, Hibernian's woes and Stuart McCall's "adventurous" Motherwell...
Celtic 2-1 Ross County
NEIL McCANN SAYS: "I don't think Stokes will replace Hooper; Hooper is more clinical and a better goalscorer, whereas Stokes is a better all-round footballer and team player who will see little reverse passes and get more assists - but he should have had a penalty against Ross County.
"I initially thought the referee, Willie Collum, got it right [by not giving a spot-kick when Brian McClean connected with Stokes] but on second view I think it was a penalty, because McClean actually pushed Stokes in the back.
"Stokes aside, I was also impressed by Kris Commons in this game - he can see a pass, is a goal threat and will be a big player for Celtic this season - and Derk Boerrigter, a player I didn't know a lot about, was good, too; he came in brilliantly from the wing to the back post, is strong, looks ridiculously quick and I think will grow into Celtic.
"Derek Adams, meanwhile, has changed around his Ross County squad dramatically, with eight or nine coming in and the same number going out, and he has to get his philosophy across to his new squad and introduce it as the games go on when they are not playing sides like Celtic.
"The Ross County on show here is not the Ross County we will see over the course of the season, and I know Derek won't say he is looking at second position but, outside Hearts and Partick Thistle, it is wide open, so why can't Ross County do it?"
Hibernian 0-1 Motherwell
ANDY WALKER SAYS: "I thought Motherwell were more adventurous; their passing was much more controlled and their change altered the match, with Anier coming on and scoring on debut - but I was surprised by Hibs' lack of adventure.
"You want to make a statement of intent on the first day of the season, especially at home, but [striker] James Collins was far too isolated and his strength wasn't utilised enough. There was a lot of fear right across the pitch and I thought they used the long ball too much, so Hibs can't have too many complaints, although their 'keeper, Williams, made some good saves.
"There is an air of depression around Easter Road and the players have to be able to deal with that and manager Pat Fenlon has to be brave in his team selection and be able to control matters ahead of the huge game next week at Tynecastle, as despite all the negativity around Hearts at the moment, they will fancy their chances of winning."
MICHAEL O'NEILL SAYS: "Hibernian will be disappointed to lose the game but more by their [lack of] intensity, the chances they failed to create, and how suspect their defence looked. The stadium was quiet, there wasn't a lot of atmosphere and it was a disappointing day all round.
"Motherwell have enough good ball handlers in the middle of the park to get control of games, while you would expect James McFadden to have greater influence on games as the season progresses, and the players brought in to replace some influential guys look capable."
Catch Hearts tackle Hibernian, live on Sky Sports 1, from midday on Sunday, August 11.