But it was a battling performance from the young Brit as she was more than a match for the former world number one in the opening set.
Robson made a confident start to that match knowing that she had taken a set of Sharapova at Wimbledon in the past.
Robson has chances to break the Sharapova serve in the fourth game but she was unable to capitalise as the Russian levelled for 2-2.
Sharapova hit back immediately as she broke Robson in the very next game to edge ahead. But Robson continued to play well and in the eighth game she got her chance as Sharapova's serve faltered.
Robson did not let her chance slip by a second time as she broke back to level the opening set to 4-4.
The partisan crowd were well and truly behind the teenager and she was able to hold her final two service games to take the opening set into a tie break.
Both players served a double fault on their opening point but it was Robson who got the early break as she opened up a 3-1 lead.
But Sharapova showed her fighting spirit as she was able to battle back and take the breaker 7-5.
Sharapova broke early in the second for a 2-0 lead but Robson looked to be getting herself back into the set when she broke back five games later.
But she was unable to hang onto her own serve as Sharapova broke again immediately to leave her serving for the match.
She wrapped up a tough 7-6 (7-5) 6-3 victory to progress into the third round
But Robson will be back on court later today as she is set to team up with Andy Murray in the mixed double competition.
There was also bad news for Heather Watson as she also crashed out of the singles competition yesterday.
She was playing 14th seed Maria Kirilenko and while she made a promising start she lost a run of three games in the middle of the first set as the Russian took it 6-3.
Into the second and things didn't get much better as Kirilenko raced to a 3-0 lead and she soon wrapped up a 6-3 6-2 victory.
FemaleFirst Helen Earnshaw