The Bhoys began the defence of their Scottish Premiership title in style, winning their first league game of the 2015-16 campaign 2-0 at home.
Both the Celtic goals came in the first half of the encounter at Celtic Park.
Leigh Griffiths put the Hoops in the lead after just four minutes when he found the target from the penalty spot, and Stefan Johansen added the second in the 35th minute.
Over the course of the 90 minutes, Ronny Deila’s side had 57% of the possession, took 13 shots of which seven were on target, and earned 15 corners.
Former Celtic striker Hartson was impressed with the performance produced by the players and highlighted how it is going to help them on Wednesday.
“It was a good win for Celtic yesterday in their opening league game of the season at home to Ross County but an expected win,” the 40-year-old wrote on Kicca.com.
“It’s good for the side to get some momentum going in to Wednesday’s Champions League qualifier against Qarabag…
“That’s their biggest game of the season, so it was a nice league to win to build up some form and travel to the game in Baku, Azerbaijan with confidence.”
Hartson was referring to Celtic’s clash against FK Qarabag away from home in the second leg of the Champions League third qualifying round on Wednesday.
The defending Scottish Premiership champions will head into the encounter with a one-goal lead, having won the first leg 1-0 at Celtic Park last week.