But Djokovic seized the match midway through the third set and then it skidded away from a classic into a coronation.
However, the third seed responded brilliantly with three breaks of serve to level the match and then stormed through the third set to prevail 4-6 6-3 6-1.
Djokovic responded by breaking twice at the start of the third set to establish a 3-0 lead and he wrapped up the set in just 28 minutes and ploughed through the fourth set to set up a third-round meeting with countryman Viktor Troicki.
Two months after losing to the Croatian at Wimbledon, Britain's number one rushed through the first set in half an hour after breaking in the third game.
Wilson passed Sebastien Bourdais midway through the race to set himself up to take his third career win.
There were no service breaks until the eighth game of the third set, when Djokovic finally broke through and then held at love to lead by two sets to one.
Soderling, who had lost all four of his previous matches against Djokovic, dropped only 11 points as he rattled through the second set and he had chances for an early break in the third.
Meanwhile Marat Safin went through to the quarter-finals when Fabrice Santoro was forced to retire in the third set.
Some good Ulster passing set Simon Danielli up for the third try before Pienaar burst through to complete the job and bag the fifth Pool Four point.
The fly-half may not have been in the best of form going into the game but he was playing beautifully and nearly set up a third New Zealand try with a lovely dummy through the England midfield.
Murray went through with a four-set win over Robert Kendrick - while Baltacha , who reached the third round in 2002, beat Ukraine's Alona Bondarenko in three sets in a late-night match.
Two-time Indian Wells champion Daniela Hantuchova saved two match points at 5-6 down in the third set of her second round meeting with Yanina Wickmayer before she edged through 5-7 6-3 7-6 (7-4).
Federer looked in danger of a third straight defeat as Verdasco breezed through the opener and threatened a massive upset in the second set.
The tougher tests awaiting New York's third-through-eighth-graders are aligned with the Common Core standards, a national set of guidelines intended to boost academic rigor.
But the Scot responded well, winning the third set 6-2 in just 33 minutes before surviving another tie break to win through in four sets in three hours and 27 minutes.
The game itself doesn't start until more than a third of the way through the book, so the there's plenty of room for Kettmann's set-up, before he goes into a virtual box score in the remaining chapters.
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