Celtic began their bid to win an eighth successive Ladbrokes Scottish Premiership title with a comfortable 3-1 win over newly-promoted Livingston at Celtic Park.
Goals from returning midfielder Tom Rogic and striker Odsonne Edouard gave the home side a comfortable interval lead with French midfielder Olivier Ntcham adding a third with a penalty five minutes after the break, rendering Scott Robinson's added time goal a mere consolation.
Brendan Rodgers' side are in the middle of their Champions League qualifying campaign and they host AEK Athens in the first leg of their third qualifier on Wednesday night.
The opening goal arrived in the seventh minute when a Hayes cross from the left found the head of Rogic, who nodded the ball past helpless goalkeeper Liam Kelly.
Celtic's second goal came from a Livi corner, Rogic racing down the pitch in a counter-attack before setting up Ntcham whose shot-cum-cross from 14 yards landed at the feet of Edouard to tap into an empty net.
Livingston's problems increased when Walsh pointed to the penalty spot after defender Declan Gallagher challenged Callum McGregor inside the box and Ntcham slotted the ball past Kelly.
Livingston managed to repel a series of more attacks and attempts on goal and as they finished with a flurry substitute Jack Hamilton, on for Miller, headed just over the bar in the final minute before Robinson forced the ball past Celtic keeper Craig Gordon at the end to give the travelling fans something to cheer.
Summer signing Peter Haring scored a double as Hearts came from behind to beat Hamilton 4-1 in their Ladbrokes Premiership opener thanks to a dominant second-half performance.
Mickel Miller opened the scoring in the 17th minute after a bright start from the hosts but, as so often happened last season, they could not hold on to their lead.
It only took Hearts three minutes to level through Haring's header and three goals in 14 minutes killed the contest by the 62nd minute with Steven Naismith and Steven MacLean also on target.
Danny Mullen struck twice for St Mirren as the Ladbrokes Championship winners celebrated their top-flight return with a 2-1 win over Dundee.
The Buddies were back in the Premiership after a three-year absence and found themselves ahead early thanks to a Mullen header.
Elton Ngwatala levelled up almost immediately but Neil McCann's men blew their chance to take the lead after the break when Sofien Moussa failed to convert from the spot.
And a gaffe from goalkeeper Jack Hamilton cost the Dark Blues dear as Mullen fired home the winner late on to provide new Saints boss Alan Stubbs a winning start.
A goal from new signing Mikael Ndjoli helped Kilmarnock win on the opening weekend of the Premiership season for the first time since 2009 as they defeated St Johnstone 2-0 at Rugby Park.
Goals from Scott Boyd and on-loan Bournemouth forward Ndjoli gave Steve Clarke's men the three points in a game of two halves.