Both seeds lost in third set tie-breaks.
Carreno Busta was beaten by Croatia's Borna Coric, 7-5, 2-6, 6-7 (8/10) in an enthralling match lasting 2 hours 41 minutes.
And Berdych went down 4-6, 6-1, 6-7 (4/7) in the match on centre court which followed against his fellow 6ft 5ins opponent, Germany's Jan-Lennard Struff.
It means the tournament has lost two of its top-ranked players after having already being shorn of three major stars -- Novak Djokovic, Stan Wawrinka and Jo-Wilfried Tsonga -- before it began, as they try to recover from injuries.
Busta's match with Coric was the game of the tournament so far.
The 21-year-old Croat, who beat Andy Murray last year at the Madrid Open, saved three match points to progress and afterwards described it as a "huge win".
"I think I played very good," he told reporters.
"I didn't know what to expect, it's the first match of the year, it's always a little bit tricky.
"But, I can say from the beginning that I was playing very good."
Coric is ranked 38 places lower than world number 10 Carreno Busta but said it was his aim to be more consistent and break into the world's top 20 this season.
"I think I can do it but I need to play very good for the whole season."
Coric had considerable success adopting a serve-and- volley approach and won 17 out of 21 points at the net in the deciding set.
Overall he hit 44 winners during the match.
He will play Nikoloz Basilashvili in the second round. The Georgian has won their previous two encounters.
The former world number four, now ranked 19th, started slowly, struggling to cope with the aggressive tactics of the big-serving Struff, the world number 53.
"My coach and me were thinking about some tactics like playing aggressive, playing with passion. Yeah, it was great," said Struff.
"I played very aggressive in the tiebreaker and I was very happy after that one."
The number five seed, Frenchmen Richard Gasquet, was untroubled by the big names falling beforehand, trouncing Victor Estrella Burgos of the Dominican Republic, 6-0, 6-2.
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