Top seed Stan Wawrinka faced just 16 minutes of tennis before reaching the third round of the Aegon Championships at Queen’s Club with withdrawing injured.
Cypriot Baghdatis, who was handed a Wimbledon wild card earlier in the day, retired with Wawrinka leading 3-2 in the first set.
World No 3 Wawrinka will now face American Sam Querrey in his first real test in the tournament.
There was also a shock exit for sixth seed Ernests Gulbis a week after his sensational run to reach the French Open semi-finals, where he lost to Novak Djokovic.
Latvian Gulbis was unable to make a smooth transition from claycourt to grass however as he slipped to a 7-6 (7/3) 7-5 straight-sets defeat at the hands of Kenny de Schepper in London.
De Schepper, ranked 66 in the world, dug in as Gulbis missed six break point opportunities as the Frenchman snatched the first set and found the all-important break claim the second set without a tie-break.
Jarkko Nieminen dumped out 12th seed Dmitry Tursunov with a straight-sets second-round victory.
The Finnish world number 62 dispatched Russian Tursunov 7-6 (7/3) 7-6 (7/3) in Kensington as the top seeds continued to fall.
Nieminen will now face eighth seed Alexandr Dolgopolov in the third round after the Ukrainian saw off Denis Istomin, prevailing 7-6 (7/3) 7-6 (9/7).
Radek Stephanek also progressed to the next stage after beating Australian Bernard Tomic 7-6 (7/4) 7-6 (7/5), while there were also straight-set successes for Sergiy Stakhovsky and Adrian Mannarino as dismissed Vasek Pospisil and Victor Estrella Burgos respectively.