Chela misses the line with an attempted pass on the next point, Murray holds.
"To beat two players of Stepanek and Chela's quality back-to-back, dropping nine games, is awesome, " said Murray.
Chela nicks the first two points of Murray's service game but Murray hits back with an ace.
Tenth seed David Nalbandian made an early exit, beaten 4-6 6-4 7-5 by fellow Argentine Juan Ignacio Chela .
Waiting for him in the second round will be Spaniard Alex Lopez-Moron or Argentinian Juan Ignacio Chela, both qualifiers.
There were no problems for fourth seed Juan Ignacio Chela who won 6-4 6-3 against German qualifier Tomas Behrend .
World number 17 Monaco is out with a back injury while Chela, ranked world number 53, has a shoulder problem.
Argentina's Juan Ignacio Chela will meet Novak in the last eight after he dispatched Spain's Feliciano Lopez 6-4 6-7 7-6.
Murray at the net now and making it 40-30 with an angled volley, but some heavy-hitting from Chela takes it to deuce.
Former world number one Carlos Moya and Argentine pair Juan Ignacio Chela and Juan Monaco withdrew earlier in the week with injuries.
Juan Ignacio Chela was leading Paradorn Srichaphan 6-3 3-0 in the first round when the Thai withdrew, and the Argentine meets Briton Andy Murray next.
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Since Andy Murray 's first loss to Juan Ignacio Chela in 2006 Aus Open, 15 sets to 1 and three straight on clay for Murray.
Murray took 67 minutes to complete his match against Chela, although at one stage it seemed like the contest would end before reaching the hour mark.
In the other matches Italy's Davide Sanguinetti overcame France's Gregory Carraz 6-3 2-6 7-5, while Robin Soderling of Sweden beat Juan Ignacio Chela, Argentina 6-4 6-3.
Knifed drop-shot from Murray on the back-hand side, but that's great scrambling from Chela to keep the game alive, yanking a backhand volley past the flailing Scot.
After requiring a fairly tortuous rain-hit two days before seeing off Juan Ignacio Chela on Thursday evening, Murray was back on court 20 hours later to face Baghdatis.
In the evening session, Britain's Andy Murray, seeded third showed improved form on clay with a 6-3 6-3 win over Juan Ignacio Chela, his fourth straight win over the Argentine.
Chela improved in the second set and he broke Murray in the sixth game, but by that point the Scot was two breaks up which proved too much to claw back.
He also came close to being broken in the eighth, but an ace secured the game before the Scot made a mockery of Chela's serve in the next to tie up the match.
Marat Safin earlier beat Juan Ignacio Chela 6-7 7-5 7-5 6-1 in the first match of the day, and Russia now just need to win Saturday's doubles to secure a place in the final.
Spanish 26th seed Marcel Granollers will play Tsonga or Mello if he defeats Portugal's Frederico Gil, while Argentina's world No. 29 Juan Ignacio Chela could face Ferrer if he gets past Spain's Pablo Andujar.
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Chela goes long on the next point before having a rustle around in his top drawer and pulling out perhaps the shot of the match, a magnificent drop-shot from about six feet behind the baseline.
Argentina's Juan Ignacio Chela completed a 6-0 6-4 7-6 (7-4) victory over American wildcard Ryan Sweeting to set up a possible meeting with Andy Murray - if the Brit can overcome an in-form Richard Gasquet on Monday.
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