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The Lions trailed Melbourne Rebels 26-5 at halftime and 33-5 early in the second half in Johannesburg.
But fueled by the high altitude at Ellis Park, which contributed to the Rebels wilting in the second half, the Lions scored four converted tries without reply to draw level.
The game was decided, thrillingly, when 21-year-old replacement Gianni Lombard landed an 82nd-minute penalty to seal a 36-33 victory.
The Reds began the comeback trend earlier Saturday in Japan.
First five-eighth Hamish Stewart kicked a last-minute penalty to see the Reds home 34-31 against the Sunwolves. It was their first win of the season.
The Reds overcame a 16-point deficit at halftime thanks to three tries in 10 minutes and four in the second half.
Brandon Paenga-Amosa scored two of the Reds' tries.
Before the match at Chichibunomiya Rugby Stadium in Tokyo, players from both teams linked arms in a circle for a silent tribute to the 49 victims of the Christchurch shootings.
The Crusaders-Highlanders game was set to follow the Sunwolves-Reds meeting, but New Zealand Rugby said the decision to cancel was taken after a meeting with the teams, venue management and police and community organizations.
The Lions, who lost the last two Super Rugby finals to the Crusaders, made a faltering start to this season and lost two of their first three games.
They looked out of it again after tries by Reece Hodge, Quade Cooper, Bill Meakes and Isi Naisarani in the first half, and another from Tom English straight after the break, took the visitors 28 points clear.
The Lions' bench came to the rescue, with Andries Coetzee and Lionel Mapoe coming on to score two of their four tries at the end and Lombard kicking a tough penalty from near the right touchline for the victory.