Despite dominating possession and chances, the Hoops required an 85th minute header from substitute Ryan Christie to secure a two-goal advantage after twice being pegged back by the Czech side.
First half goals from Liel Abada and Kyogo Furuhashi put Ange Postecoglou's men into a commanding 2-0 lead before Vaclav Pilar raced through a static defence to pull one back for the hosts before half-time.
James Forrest restored the two-goal cushion in the second half but Tomas Malinsky lobbed debutant goalkeeper Joe Hart to reduce the deficit again before Christie struck to give Celtic breathing space ahead of next week's second leg at Parkhead.
Ex-Celt Hartson felt the margin of victory should have been greater as he slammed the standard of defending at both Jablonec goals, with new signing Carl Starfelt singled out for criticism.
"It's a good away win but they could have been out of sight," he said. "Celtic had an opportunity to win by four or five, all they had to do was defend properly.
"It's Sunday league stuff. The goals that they are giving away. Celtic won't win anything defending like that.
"I know it will get better and Jullien might come in back, but Starfelt at the second goal ... I know he's early at the club but I have to call it as I see it. You can't just dive in last minute and let Malinsky cut back inside like that and just get done.
"He lobs Joe Hart, maybe the defence was coming back but should he be that far off his line?
"Normally I'm not overly critical, but I can't sit here and accept that type of defending. It's going to cost Celtic."
Speaking on BBC Sportscene, Hartson was also critical of Celtic's failure to take chances, despite scoring four.
"We're not putting teams to the sword. How many opportunities do Celtic need to go and score goals at this level?
"Luckily the scoreline looks quite respectable now at 4-2 because Ryan Christie comes on and scores a really good header.
"Celtic will get through next week but I worry badly about our defence."