Williams breezed through the first set and then relied on her powerful serve in the second. She did not face a break point in the entire match, losing only nine points on her serve.
Silva sent a shot wide to set up two match points for Williams, who converted the first one when her Portuguese opponent netted a backhand.
"I could have played a ton better, especially on key points," Williams said. "That's a usual feeling for me from first round to the finals. I'm really insatiable. I always want more."
The No. 2-seeded Williams, runner-up to sister Venus a year ago, improved to 5-5 since starting the year 21-2.
"I'm just happy to have a win under my belt here," Williams said. "I was a little nervous going into the match."
Williams is looking for her third Wimbledon title, while the 154th-ranked Silva was making her main-draw debut.
Maria Sharapova overcame a poor start to beat Viktoriya Kutuzova in the first round, rallying from two breaks down in the first set before winning 7-5, 6-4.
The former top-ranked Russian trailed 4-1 and 5-3 in the first set before winning the last four games.
Both players struggled to hold serve in the second. Sharapova broke Kutuzova for a 5-3 lead to serve for the match but was broken at love. The 2004 champion then broke again, converting her first match point when Kutuzova netted a backhand.
As a precautionary warm-up for her shoulder, Sharapova has taken to throwing around a football to loosen the joint before practice sessions. And she has adjusted her service motion, a change that she acknowledges is something of a work in progress.
How long will it take to get her serve up to speed?
"Definitely time; I don't know how long. I don't know how long 'til everything comes together," she said. "That's why I'm here. If I knew, maybe I wouldn't be here. If I knew it wasn't going to be at this tournament, maybe I'd be home just waiting 'til I knew when it would come."
The match as a whole was tighter than the final score might indicate: Sharapova won only five more points than her opponent, 69-64. Footing seemed to be a bit of an issue for Sharapova, who tumbled to the grass behind the baseline once in each set, banging a knee each time.
Still, Sharapova figured she could take something positive out of the way she turned things around after the slow start.
"Look, I hung in there," she said. "If she was able to continue at the level that she was playing in the first few games -- where she was just swinging away, everything was deep and hard -- sometimes it's just too good. But, you know, I was able to give her a little bit of her own medicine."
Sharapova used to be ranked No. 1. But time off the tour for shoulder surgery dropped her outside the top 100. She has climbed back to No. 60, and her past success at Wimbledon led the tournament to seed her 24th.
Pleased as she might be to be here, one victory this year at the All England Club is not exactly going to satisfy Sharapova.
So she'll be on the practice courts soon enough, football in tow.
"There are definitely things I'm going to be working on the next day or so. But that's always the case at every single tournament," Sharapova said. "I mean, if you feel perfect, then there's something wrong."
Robson, the youngest player to contest the main draw since Martina Hingis in 1995, made the ideal start by opening the match with an ace before wrapping up the first set in 38 minutes.
But Robson, the girls' champion last year, gifted the former world No. 5 the second set with two double faults serving at 4-5 and the teen's game deserted her in the tiebreak.
She saved the first match point with a defiant ace but then another double fault handed the Slovak a second-round berth for the ninth straight year.
She will play 16th seed and semifinalist last year, China's Zheng Jie, for a place in the third round.
No. 4 Elena Dementieva, No. 8 Victoria Azarenka, No. 10 Nadia Petrova, No. 12 Marion Bartoli, No. 14 Dominika Cibulkova, No. 26 Virginie Razzano, No. 27 Alisa Kleybanova, No. 28 Sorana Cirstea and No. 31 Anastasia Pavlyuchenkova advanced. No. 21 Patty Schnyder and No. 23 Aleksandra Wozniak were eliminated.
Information from The Associated Press and Reuters was used in this report.