Forrest then replaced Kris Commons, who came off with a hamstring injury which must make him doubtful for Europe, and a moment of magic in the 75th minute by the Scotland winger deservedly levelled the scores at Easter Road.
Celtic face Ajax still looking for their first points after two games and they will have to do so without skipper Scott Brown, who was handed a three-match ban after getting sent off against Barcelona at Parkhead earlier in the month.
Although the Scottish champions have indicated they will appeal, the automatic one-game ban rules him out of the visit of the Dutch side.
Aside from concerns over Commons, left-back Emilio Izaguirre was out of this contest through illness.
Lennon will also be without Adam Matthews, out for three months with a shoulder injury and his right-back rival Mikael Lustig, who also missed the trip to Leith, is a doubt with a hip complaint.
To that end, the Parkhead boss was forced to give 19-year-old Darnell Fisher his competitive debut and he had some early touches in a scrappy beginning.
In the 14th minute Commons broke up the monotony of mistakes when he tried a speculative drive from 25 yards but the ball flew over the bar and moments later his header from Brown's cross went equally astray.
It looked like the champions were finding their feet but Hibs forged ahead with their first chance.
Celtic's Dutch defender Virgil van Dijk's loose pass out of defence saw Hibees midfielder Kevin Thomson winning a tackle with Brown to send the unmarked Heffernan through to shoot past Forster.
There was a hint of offside about the goal but it energised the home side, who sensed there might be a second for the taking.
However, five minutes later Commons had another chance when he ran through on goal but although his chip beat Hibs keeper Ben Williams it also cleared the bar.
The Hoops midfielder was soon replaced by Forrest and Celtic began to turn the screw.
On the half-hour mark Georgios Samaras had a side-footed shot from 14 yards saved by skipper Williams after being set up by Teemu Pukki, with former Easter Road striker Anthony Stokes then hitting the side-netting.
Three minutes from the break Hibs defender Ryan McGivern's lunging block prevented Pukki drawing Celtic level with a close-range shot.
It was no surprise that the Glasgow side came flying out of the traps after the break.
Four minutes into the second half Williams made a fine save from Beram Kayal's low drive from the edge of the box with stopper Michael Nelson completing the clearance.
As the pressure intensified Williams made another save, this time from Stokes at his near post with the corner coming to nothing.
Heffernan continued to look dangerous on the break but in the 65th minute it was Owain Tudur Jones who tested Forster with an effort from the edge of the box after being set up by Abdellah Zoubir.
The pressure on the Hibs penalty area refused to subside but it was a wonderful goal to which they succumbed, Forrest driving into the box and curling the ball with the outside of his right foot past Williams and into the far corner on his return from sciatica and virus problems,
Stokes missed another chances moments later, volleying wide after being picked out by Forrest, who - with three minutes remaining - saw a close-range volley brilliantly saved by Williams.
Lennon will have been pleased with his side's spirited comeback but will now have to regroup ahead of the Ajax game - which will shape their future in Europe this season.
Meanwhile an 89th minute goal from Steven Thompson settled a thrilling contest as St Mirren picked up their first win of the season against St Johnstone in a 4-3 goal feast.
Goals from Kris Boyd and Jackson Irvine gave Kilmarnock boss Allan Johnston his first win since taking over at Rugby Park in the summer.
The 2-0 home victory over Ross County eased the pressure on the former Queen of the South manager but there were yet more protests as the Killie fans continued to heap flak on chairman Michael Johnston.
Calvin Zola's close-range strike early in the second half was enough to see Aberdeen seal a 1-0 victory over Dundee United at Pittodrie.
And Craig Moore scored a spectacular goal seconds into his Scottish Premiership debut to start Motherwell's comeback as Hearts slipped further behind at the foot of the table after a 2-1 loss.