Djokovic battles past Baghdatis
The world number one took his total number of wins this season to 67 by extending his unbeaten run against Baghdatis to six matches.
The Serb will now face Kei Nishikori in Saturday's semi-final as he bids to reach the final in Switzerland for the third consecutive year.
Djokovic - playing in his first tournament since he was forced to retire from his Davis Cup tie against Juan Martin del Potro in September - began sluggishly and Baghdatis took full advantage.
Despite the former world number eight now languishing at 59 in the rankings, the Cypriot showed why he is so popular wherever he goes on the ATP Tour by breaking Djokovic in the very first game.
Baghdatis's previous two matches in Basel had both gone the distance, perhaps explaining the glut of second serves and double faults he was delivering, but Djokovic failed to capitalise and was punished by being broken again in the seventh game, courtesy of a two-hander drilled down the line.
Djokovic gradually got himself into gear in the second set, and this time he did take advantage of Baghdatis's poor service game by breaking him in the sixth and eighth games thanks in part to more double faults.
The 2009 champion then broke his flagging opponent at the first opportunity in the deciding set and did not relinquish his lead.
Djokovic will face Kei Nishikori in the semi-finals after the 21-year-old Japanese beat Kazakhstan's Mikhail Kukushkin 6-4 5-7 6-4.