After Andy Murray's efforts in battling back from deficits to win in five sets in rounds one and two of the French Open, it looked like British No.2 Bedene might go the other way.
He took the opening two sets against Spaniard Carreno Busta in fine style but then saw the world No.43 hit back to level.
Carreno Busta had the momentum going into the decider but it was Bedene who came through 7-6(4), 6-3, 4-6, 5-7, 6-2 after winning the last four games.
Djokovic, meanwhile, saw off Steve Darcis to set up only a second career meeting with Bedene. The world No.1 won their only previous match in the first round of the Australian Open last year.
Like he had in the first round against qualifier Gerald Melzer, Bedene made a slow start but again he retrieved the early break and battled manfully to hold onto his serve in the sixth game, saving five break points. He made a brilliant start to the tie-break, winning the first five points, and, although he lost the next three, he got over the line.
Bedene came into the tournament happy with his form but low on confidence amid the stress of his ongoing battle to represent Great Britain in Davis Cup.
He is also without a coach, although praised the influence of Davis Cup captain Leon Smith, who is helping him out on a temporary basis.
Bedene looked supremely confident in set two, winning the final four games, but Carreno Busta made a good start to the third set and the momentum turned.
Bedene had two chances to take the fourth into a tie-break but could not take them and there was then a long break while Carreno Busta received treatment to his left thigh.
The initial stages of the decider were tight and tense but Bedene forged ahead with a break for 4-2 and thereafter the end was swift, with the 26-year-old letting out a huge roar after Carreno Busta's final backhand landed wide.
Murray spent a brief spell as world No.1 this spring, the first British player ever to officially stand at the top of the rankings. The Scot currently sits third behind Marcelo Melo and Nicolas Mahut but it is very tight and a good run in Paris could see him regain top spot.