Georgios Samaras's last-gasp header in the Luzhniki Stadium gave the Hoops their first win away in the group stages of European football's elite club competition.
Gary Hooper shot the visitors into the lead in the 12th minute before Emmanuel Emenike netted twice for the Russian club, once either side of the break.
Spartak defender Juan Insaurralde was sent off just after the hour mark for preventing Hooper going clean through on goal before Celtic levelled after a drive from substitute James Forrest deflected in off Spartak captain Dmitri Kombarov.
In the dying seconds Samaras headed in an Emilio Izaguiire cross to send the small band of Hoops fans - and the Celtic bench - wild with delight.
"I think people underestimate Celtic," said the Celtic boss.
"I don't think we get the respect we deserve but maybe last night's [Tuesday] performance might change a few attitudes."
Celtic are in second place in Group G with four points after two games ahead of their double-header against Barcelona, who top the group with maximum points from their first two fixtures after beating Benfica 2-0 last night.
However, Lennon refused to get carried away with regards his side's chances of qualifying for the knockout stages.
The former Celtic skipper said: "We just have to play Barcelona home and away...
"But it was a huge step for the club.
"It was our first away win in the Champions League so we have broken a record.
"It is fantastic but there is a lot of football to be played in the group.
"We have two home games and Benfica and Barcelona away so it is still an open group for second place as far as I am concerned."
Meanwhile, Hooper will try to bring himself back down to earth after his performance was described as "world class" by Lennon.
The Parkhead striker grabbed his seventh goal in four games which also inspired his manager to reiterate his belief that the Essex boy should be on the radar of England boss Roy Hodgson.
Hooper tried hard to digest Lennon's praise as he looked towards Sunday's Clydesdale Bank Premier League game against Hearts.
"It is amazing," he said. "After the performance and the gaffer saying that, it feels really good.
"I have to try to take myself down and go again on Sunday."
As for a possible England call-up, Hooper said: "I want to play for England but is it not my decision, it is out of my hands,
"I have to keep doing it on the field, like I did last night, and against Raith and Motherwell recently and hopefully on Sunday and let them (England) decide."