The French side went through after Ajax Amsterdam, who started the night three points ahead of them with a vastly superior goal difference, were beaten 3-0 at home by group winners Real Madrid.
Lyon's challenge looked all but over when they fell behind to a Mateo Kovavic goal in the 40th minute, after Dinamo had their midfielder Jerko Leko sent off for a second bookable foul midway through the first half.
But the French side's striker Bafetimbi Gomis led their revival with four goals, with Maxime Gonalons, Lisandro Lopez and Jimmy Briand netting the other three to send them into the last 16 of Europe's premier club competition.
Gomis's first three goals in the space of seven minutes either side of half-time are a Champions League hat-trick record.
"The game took an unbelievable turn after the interval and it all happened so quickly in the second half that we didn't really have time to follow whether the result in Amsterdam was going our way," Lyon manager Remi Garde told a news conference.
"We knew at half-time Ajax were 2-0 down and that gave us the strength to believe that we could do the impossible and overhaul them to the runners-up spot on goal difference," he said.
Gomis bundled in the equaliser on the stroke of half-time and the floodgates opened after the break as Lyon, who fielded a 4-3-3 formation with Briand and Alexandre Lacazette up front alongside the robust striker, came out with all guns blazing.
QUICKFIRE TREBLE
They needed just six minutes to haul themselves back into the hunt for a berth in the knockout stage with three simple goals as Dinamo's numerical disadvantage in freezing weather started to bite.
Gonalons steered home a corner which was nodded into his path in the 48th minute before Briand robbed a defender of the ball almost straight from the restart and squared it for Gomis to hit the empty net from 13 metres.
Gomis was on target again in the 51st minute after Aly Cissokho raced down the left flank and delivered a sharp low cross which the galvanised hitman tapped in from close range.
Lyon's incessant pressure carved out another chance for Gomis on the hour, when he hit the post with an acrobatic volley, before second half substitute Lisandro made it 5-1 with a clinical finish in the 64th minute.
Man of the match Gomis scored his fourth just five minutes later, side-footing yet another superb cross by Cissokho into the top left corner past the despairing reach of Ivan Kelava.
Briand then made it 7-1 when he placed the ball past Kelava from the edge of the penalty area after a defence-splitting pass from the halfway line put him through.
Jubilant Lyon players and Garde celebrated their biggest Champions League win while Dinamo were jeered off the pitch by angry home fans after suffering their heaviest defeat in all European competition.
"Of course we are absolutely delighted to have earned a berth in the last 16 and it was very difficult for Dinamo to keep their spirit up after conceding so many goals in such a short period of time," Garde said.
His counterpart Krunoslav Jurcic acknowledged Dinamo had a long way to go if they are to become a competitive Champions League side.
"We are a very young team and this was the first time any of these players have been involved in the Champions league, so we obviously have a lot to learn," he said.
"It's a very painful defeat but if we take it the right way we will benefit in the long term because it is now apparent how hard we have to work in order to improve and be more competitive the next time we qualify."
