The two-time champion, who recorded his 16th consecutive victory at tennis' most prestigious event, dropped serve only once and dominated the baseline rallies to take the match in just over two hours.
Unlike on Monday, when he went down an early break of serve against American Michael Russell before finding his form, Nadal quickly took a 3-1 lead against Sweeting and never looked back.
The American's surprising lack of aggressiveness did not help his cause.
In the first set, Sweeting only came to the net one time and lost that lone point. Throughout the match, the American was also reluctant to serve and volley and that allowed Nadal to comfortably get his opponent's serve back in play with soft floating chip returns and then win the ensuing baseline rallies.
Nadal, meanwhile, was his typically efficient self, winning seven of eight net approaches in the early stages en route to a solid first set win. He then broke early in the second set and the rout was on.
Sweeting got down a break in the third set before managing to steal a break back with a forehand volley winner, but Nadal wasted no time seizing back the advantage with a perfectly executed backhand crosscourt passing shot.
"It was a good match. I was playing very well," the 25-year-old world No. 1 said in the post-match interview, adding that he benefited from a "few mistakes" from Sweeting.
It was the first time Nadal had played on Center Court under the retractable roof, inaugurated in 2009. The entire match was played indoors even though the rain stopped during the match.
Nadal has not lost at Wimbledon since his five-set defeat in 2007 at the hands of Swiss great Roger Federer, although he did not compete in the 2009 event due to injury.
In other men's second round action Wednesday involving Spanish players, Fernando Verdasco was upset by Dutchman Robin Haase 6-3, 6-4, 4-6, 6-2 and Feliciano Lopez defeated Germany's Rainer Schuettler 7-6 (7-3), 6-7 (3-7), 6-2, 6-2.
In Friday's third round play, Nadal will face Luxembourg's Gilles Muller, who advanced when his opponent, promising Canadian Milos Raonic, defaulted with a serious leg injury. The 28-year-old Muller stunned Nadal at Wimbledon six years ago, when the Spaniard was still a teenager.
Lopez, meanwhile will take on big-serving American Andy Roddick, a three-time finalist, also on Friday.
The lone member of the Latin American men's contingent in action Wednesday, Argentina's Juan Ignacio Chela, the No. 25 seed, lost to American Alex Bogomolov Jr. 6-0, 6-3, 6-4.
Wimbledon is the third of four Grand Slam events on the tennis calendar and the only one played on grass.