Baltacha – the British No 1 – lost in a closely-fought three-set thriller with 20th seed Peng Shuai, while 17-year-old Robson gave former champion and this year’s title favourite Maria Sharapova a scare on Court One.
Robson made the perfect start and raced into a 4-1 lead but Sharapova broke back to draw level before taking the set into a tie-break.
Sharapova, who was Robson’s age when she won the title here in 2004, then had to come from a mini-break down to claim the opening set.
The Russian stepped up a gear in the second set and opened a 5-1 lead but Robson showed real heart to keep battling and broke Sharapova’s serve to stay in the match.
Eventually, Sharapova, the three-time grand slam champion, prevailed 7-6 (7/4) 6-3 and she will now face Klara Zakopalova.
After plucky first-round defeats to Daniela Hantuchova in 2009 and Jelena Jankovic in 2010, Robson, the world No 254, won her first grand slam match on Wednesday, beating Angelique Kerber in three sets.
After a nervy start Robson remained composed and eventually held serve in a nine-minute opening game.
Robson’s forehand was proving to be a real weapon – she hit six winners with it in the first two games – and she raced to 15-40 on Sharapova’s serve.
The Russian took it back to deuce but her serve was malfunctioning and consecutive double faults gave Robson the early break and a dream start.
Robson consolidated the break confidently and was asking questions of Sharapova as she opened a 4-1 lead. But the Russian broke back with a crunching backhand out wide that Robson could only return into the net and the set was soon all square at 4-4.
Robson ended a run of three lost games on the back of some powerful serving and she was mixing her game up well, combining blistering forehand winners with a deft drop shot. Sharapova took the set into a tie-break and then had to come from a mini-break down at 4-2 to win it.
The Russian fifth seed then began to assert her authority at the start of the second set, breaking Robson at the first opportunity to move 2-0 up.
Robson, typically, refused to go down without a fight and she broke straight back, but that only prompted Sharapova to step up another gear and she broke Robson to love with some ferocious groundstrokes and then opened a 4-1 lead with three aces.
Suddenly the 248 ranking places that separated the two players began to show as Sharapova moved a second break up and served for the match. But Robson would not concede defeat without a fight.
She broke back as Sharapova served for the match and then worked another break point at 5-3 but Sharapova snuffed out hope of a dramatic comeback.
Baltacha was left to rue a missed opportunity after she was edged 4-6 6-2 7-5 by Peng, from China, on Court 18.
The omens looked good as Baltacha made a strong start, showing variety in the third game in the shape of a drop shot and booming forehand to secure a break point that Peng saved with a superb crosscourt winner.
Danger followed in the fourth when Baltacha was forced to save three break points, with one coming after a rally of dynamic volleys at the net. Play settled down until the ninth game when Baltacha seized the chance to make the crucial move in the set.
Amassing three break points after outplaying Peng, she capitalised on the first with an inch-perfect forehand to the right corner that left her opponent flailing.
Three set points followed in the 10th as her serve found its mark with clinical efficiency, with Peng finishing an extended rally by hitting long.
Peng was having to work for every point but in the fourth game of the second set she was able to strike, capitalising on some weak serving to break.
A lengthy rally in the fifth ended with a neat winner from Peng and the initiative was slipping away from Baltacha.
It was Peng’s turn to dictate play and she broke the fading Baltacha in the eighth game with the Briton repeatedly finding the net.
Baltacha exploded back into life in the opening game of the final set, her mind clearly refocused as she out-hit Peng to claim the third of three break points.
Urging herself on, she seemed a different player – only to then collapse from a commanding position on her own serve in the next game with a double fault and shot into the net.
An unpredictable third set continued apace with Baltacha squandering four break points in the third as the tension mounted.
She was more ruthless in the fifth, playing intelligently and with great poise to break once more and regain the initiative.
The opportunity to go 5-3 up vanished in a blink as nerves suddenly ate away at the aggression that had served her so well, with Peng breaking back.
Serving to stay in the match in a marathon 12th game, there was an air of inevitability about the outcome as Baltacha came off worse in a high-quality rally to concede match point.
That was saved, as were two more, but she blasted into the net on a fourth as the door into the third round slammed firmly shut for the determined and impressive Scot.