The victory makes the 38th-ranked Robson the first British woman to advance to the Round of 16 since 1998.
The 19-year-old former Wimbledon junior champion, playing on Court Two, was three points from losing in straight sets, having dropped the first set to the 71st-ranked Erakovic.
Robson's latest major breakthrough is the second time she's reached a Grand Slam Round of 16, having done so at last year's US Open. She will face either Kaia Kanepi of Estonia or American Alison Riske in Monday's fourth round.
Also on Saturday, American Sloane Stephens reached the fourth round for the first time, coming back to close out an uneven 7-6 (3), 0-6, 6-4 victory over 196th-ranked qualifier Petra Cetkovska of the Czech Republic.
Resuming at the start of the third set, the 17th-seeded Stephens fell behind 2-0, but Cetkovska double-faulted three times while letting the American take a 4-3 edge.
Stephens is in the round of 32 for a third consecutive Grand Slam tournament. At the Australian Open in January, she defeated Serena Williams en route to the semifinals.
In other Saturday matches, Bernard Tomic reached Wimbledon's fourth round by upsetting No. 9 seed Richard Gasquet 7-6 (7), 5-7, 7-5, 7-6 (5).
The 20-year-old Australian, who's ranked 59th, saved 7 of 8 break points and hit 19 aces.
His father, John Tomic, was barred from Wimbledon while his court case is pending in Madrid, Spain. He is accused of head-butting Tomic's hitting partner.
Tomic's best Grand Slam showing came at Wimbledon in 2011 as a qualifier, when at 18 he was the youngest player to reach the tournament's quarterfinals since Boris Becker in 1985.
Petra Kvitova avoided becoming the latest former champion to be knocked out in the first week at Wimbledon, rallying from a break down in the final set to beat Ekaterina Makarova of Russia 6-3, 2-6, 6-3 and reach the fourth round.
The match had been halted Friday with Makarova up 2-1 in the third set, but the eighth-seeded Kvitova broke right back when play resumed and won the next two games as well. After losing her own serve, the Czech player broke again for a 5-3 lead and then converted her third match point with a forehand winner.
"It was another day for me," Kvitova said. "I played really well. I should go for every point and play my game. So I played quite aggressively. That was the key."
Kvitova won Wimbledon in 2011 but has struggled to match that performance since and has slipped from second to eighth in the rankings. She has a good chance of reaching her second final at the All England Club, however, having seen second-seeded Victoria Azarenka and former champion Maria Sharapova already eliminated on her side of the draw.
"It's still so far away," Kvitova said. "I'm the highest-ranked player [left] in my half, but there's still a lot of great players over there."
To have a chance at another title, though, Kvitova said her consistency has to improve.
"In 2011 I played really well. I mean, I play my best, for sure. Every shot was going to the court," she said. "It's not the same this year. ... I drop off little bit. It's always little bit up and down, but I hope it will be more up than down."
Later Saturday, top-ranked Novak Djokovic and Serena Williams were set to play their third-round matches, also looking to avoid further upsets after seven-time champion Roger Federer and Rafael Nadal were both eliminated early.
Because of rain over the last two days, Wimbledon organizers were playing a bit of catch-up with the schedule on Saturday, before Sunday's rest day.
Among several other matches that had been postponed, No. 20 Mikhail Youzhny of Russia beat Viktor Troicki 6-3, 6-4, 7-5 to set up a fourth-round meeting with second-seeded Andy Murray, who won in straight sets on Friday.
Two more seeded players went out against unseeded opposition, as No. 22 Juan Monaco of Argentina fell 6-4, 7-6 (8), 6-4 to Frenchman Kenny De Schepper, while No. 26 Benoit Paire of France lost 6-1, 6-3, 6-4 to Lukasz Kubot of Poland.
No. 23 Andreas Seppi of Italy kept up his perfect record in five-set matches in 2013, winning his seventh straight by defeating 12th-seeded Kei Nishikori of Japan 3-6, 6-2, 6-7 (4), 6-1, 6-4. Seppi also beat Denis Istomin in five sets in the first round, and won two five-setters each at this year's Australian Open and French Open. He also rallied from two sets down in a Davis Cup match this year.
As is traditional on the middle Saturday of the tournament, the Royal Box on Centre Court was filled with a number of invited sports stars, this year mainly British gold-medal winners from the London Olympics. Among those getting the biggest ovation from the crowd were cyclists Chris Hoy and Victoria Pendleton -- as well as Murray, who donned a suit and tie to make a brief appearance in the box to celebrate his singles gold medal won on Centre Court.