With the Bulgarians tied at 1-1 on aggregate in the play-off round against Steaua Bucharest, regular shot-stopper Vladislav Stoyanov brought down the visitors' Fernando Varela in the 119th minute, prompting a red card from Spanish referee Alberto Undiano.
And with all three substitutions having been used up, the home side were unable to bring on reserve keeper Ivan Cvorovic.
But Moti, a Romania international, took over the goalkeeping duties for the dying seconds of extra-time and the resulting penalty shoot-out and produced a remarkable match-winning display between the posts.
He went on to net the opening penalty before making two dramatic saves from Paul Parvulescu and Cornel Rapa to secure a 6-5 victory on spot-kicks, sending the home crowd into raptures.
Ludogorets had earlier appeared to be heading out of the competiton as a result of their 1-0 first-leg defeat, only for substitute Wanderson to score a crucial 90th minute goal to send the match into extra-time.
Moti's heroics mean Ludogorets will line up in the Champions League group stage for the first time in their history, with six games against some of the biggest names in Europe a reward for their exploits so far.