Mubarak Wakaso scored 14 minutes into his Hoops debut but Brazilian striker Alan levelled 10 minutes from the break with a shot from the edge of the box which took a marked deflection off Efe Ambrose before looping over Craig Gordon,
On the hour mark Hoops captain Scott Brown, playing only his second game of the season after recovering from a hamstring injury, sent in a drive from outside the box which hit Andre Ramalho and the ball spun into the net.
Gordon made several saves, a couple of them brilliant, to keep the home side at bay but he had no chance in the 77th minute with skipper Jonatan Soriano's 25-yard free-kick which flew high into the top corner.
However, manager Ronny Deila will probably see this as a decent result against the top seeds as he prepares to face Dinamo Zagreb next month with Romanian outfit FC Astra also in the section.
Salzburg's 32,000-capacity stadium was less than half-full at kick-off with the few hundred Hoops fans who made the trip seeing Wakaso for the first time.
The Ghanaian winger, on loan from Rubin Kazan, made a dream start to his Hoops' career
He did not break stride as he ran on to a Kris Commons pass at the edge of the box and sent a left-footed shot past Salzburg keeper Peter Gulacsi and in at the far corner
It was a body blow for the home side who had started the better but they upped the pace and came close when midfielder Kevin Kampl curled a shot wide from the edge of the box after being set up by Christoph Leitgeb.
The game opened up further.
Gordon made a decent save down at his right-hand post from Soriano.
In the 31st minute the Hoops number one then made a brilliant finger-tip save from Ramalho after the Salzburg defender had escaped the Hoops defence to get his head on to a Soriano free-kick, the resultant corner coming to nothing.
The Salzburg pressure mounted but their equaliser owed much to good fortune when Alan's shot from the edge of the box, after he had been played in by Kampl, struck the luckless Ambrose and sped past Gordon.
The Scottish champions were looking for the respite of the half-time whistle but before then midfielder Marcel Sabitzer fired wide from the edge of the box.
Four minutes after the break Gordon made yet another fine save, this time pushing Alan's powerful drive round the post for a corner, which came to nothing.
In the 52nd minute Hoops striker Stefan Scepovic tried his luck with a long-distance punt and came within a couple of feet of scoring a remarkable goal.
However, that incident was out of kilter with proceedings.
Three minutes later Gordon came to Celtic's rescue again with a double-save, first parrying a drive from Sabitzer into the air and then somehow clawing away Alan's close-range header from the loose ball.
Against the run of play, Celtic took the lead.
Ramalho thought he had done his job when he headed clear a Callum McGregor cross but watched Brown smash the ball back at goal, taking a nick off the Brazilian defender to wrong foot Gulacsi.
Anthony Stokes replaced Scepovic after 67 minutes but Salzburg came back again, Alan skimming the outside of the post with an effort from the edge of the box.
There was no surprise when Salzburg levelled although Soriano's free-kick, after Emilio Izaguirre had fouled Sabitzer, was perfectly-executed, giving Gordon no chance.
Source : PA
Source: PA