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Steven Gerrard's nine-man Rangers survived a frantic second-half Ufa onslaught to clinch a place in the Europa League group stage.
The Scottish Premiership side remain unbeaten in 12 games under Gerrard despite playing the final 24 minutes with a two-man deficit after Jon Flanagan received a second booking.
Alfredo Morelos had earlier been shown his second red card of the campaign - this time being given a second yellow for dissent after being cautioned for kicking the ball away.
At that stage, Rangers were ahead 2-1 on aggregate after Ovie Ejaria's curling shot was cancelled out by Dmitri Sysuev's leveller.
Ufa registered 26 attempts as they pushed late on but they found Allan McGregor and his defence a formidable barrier, with an injury-time strike ruled out for offside.
Rangers now visit Celtic in Sunday's Old Firm game having reached the group stage of a European competition for the first time since the 2010-11 Champions League.
The draw takes place in Monaco on Friday at 12:00 BST.
Nobody could have foreseen the nervy second half that would befall Rangers when Ejaria's stunning opener put the Glasgow outfit into the lead on nine minutes.
Flanagan's cross was not dealt with by the Ufa defence and the on-loan Liverpool defender curled his shot high into the net from just inside the box to leave the Russians needing three goals to prevent the Premiership side reaching the group stage.
Rangers had not conceded a goal away from home in three European ties this season until Sysuev struck on 33 minutes - running in on goal and slotting beyond McGregor despite looking marginally offside.
The equaliser caught the Scottish side by surprise, and was one of the few times Gerrard's defence appeared vulnerable at the Neftyanik Stadium.
Ufa still needed two more goals, but the tie appeared to take an even more ominous turn on 38 minutes.
Morelos was booked for kicking the ball away after being penalised for a challenge, and a second yellow followed after he directed his frustrations towards the officials.
It was the Colombian striker's second red card of the season, having been dismissed for a kick at Aberdeen's Scott McKenna in the opening game of the season, albeit the punishment was later downgraded to a booking.
That left Rangers facing just short of an hour with a man disadvantage and their task became even more daunting on 66 minutes, when referee Tobias Stieler penalised Flanagan for a high elbow.
Then the Ufa cavalry charge began. Vyacheslav Krotov hit a post and Jemal Tabidze had the ball in the net in injury time, but it was ruled out for a foul on Ejaria.
Rangers defended desperately, though, and did enough to ensure European football until Christmas.
Former Rangers & Scotland striker Billy Dodds on BBC Sportsound
The biggest disappointment is that Morelos had so many opportunities to get himself out of the situation and ensure he stayed on the park but he didn't take them. It's so selfish and he put his team in a lot of trouble.
People were asking the question of Steven Gerrard and whether he was tactically good enough. He's answered a huge question. Rangers rode their luck at times but it was a brilliant performance.
Referee:
Tobias Stieler
