Jon Flanagan was also dismissed during the second half to leave Rangers looking to avoid conceding two further goals with nine men, but Steven Gerrard's team held on to earn a place in the main stages of a European competition for the first time since 2011.
Rangers had made the perfect start in Russia, with Ejaria collecting the ball just inside the area before curling a shot into the top corner of the net from 16 yards out.
The Scottish giants continued to have the better of proceedings heading towards the half-hour mark, and after Connor Goldson had to make a goal-saving block at the opposite end, Ejaria was denied a second by a fine save from Aleksandr Belenov.
However, Ufa soon levelled the match on the day as Sysuyev got on the scoresheet, and things quickly went from bad to worse for Rangers as Morelos was dismissed for back-to-back yellow cards picked up for kicking the ball away and dissent.
Rangers welcomed the half-time whistle but soon after the restart, the visitors almost netted a second goal as Ryan Kent was superbly kept out by Belenov.
Ufa soon began to get on top, however, and their cause was aided when Rangers were reduced to nine men with Flanagan also being sent off for two bookings.
Rangers were left with little option but to keep their eight outfield plays behind the ball in an attempt to see out the remainder of the contest, but Ufa continued to press hard with goalkeeper Allan McGregor having to make a stunning block from Sylvester Igboun.
Substitute Vyacheslav Krotov struck the base of the post in the final minute of normal time, but Rangers survived to earn one of their most famous results in their recent history.
FC Ufa Belenov, Tabidze, Alikin (Oblyakov 52'), Nedelcearu, Zhivoglyadov, Salatic (Krotov 76'), Paurevic, Jokic, Vanek, Sysuev, Igboun
Rangers McGregor; Tavernier, Goldson, Katic, Flanagan; Candeias (Lafferty 46'), Jack, Ejaria, Arfield (Halliday 69'), Kent; Morelosbody check tags ::