Nadal, seeded fifth, won 6-3 7-5 and will next face long-time rival Federer or American Steve Johnson.
But he's got a monumental task in Indian Wells, where he anchors a bottom quarter that also includes four-time champion Roger Federer, and three-time victor Rafael Nadal.
Pliskova, a 2016 semi-finalist, will play French Open victor Garbine Muguruza, who beat Elina Svitolina 7-6 (7-5), 1-6, 6-0 and ended the Ukrainian's 15-match win streak. The two have had a number of exciting encounters at the Masters 1000 tournaments and their match at the Indian Wells Masters will be expected to be as exciting as the Australian Open final a few months ago which Federer won.
The world No 2, who has not been beaten at this tournament since a defeat to Del Potro in 2013, got the better of his opponent this time around, winning 7-5, 4-6, 6-1.
"I didn't try to do fantastic things. So I think the match will be played a bit different", he added. I think that's the most incredible thing about his game.
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Left-arm spinner Mohammad Asghar and allrounder Fahim Ashraf round out the group of five uncapped players picked in the squads. Former ODI skipper Azhar Ali has lost his place in the squad after a poor run of form both as a batsman and as captain.
Among Thursday's matches, Italy's Paolo Lorenzi downed Robin Haase of the Netherlands to book a first-round meeting with third-seeded Swiss Stan Wawrinka. To add to the excitement, the victor of the match between Nadal and Federer will take on either Djokovic or Kyrgios in the quarter-finals.
The 46th-ranked Edmund served for the second set at 5-3, but world number two Djokovic broke him en route to a 6-4, 7-6 (7/5) triumph.
While Nadal and Tomic are out of the running in the doubles at Indian Wells, Australian Nick Kyrgios and Serbian Nenad Zimonjic are through to the quarter-finals.
"I played much better than the first day".
Novak Djokovic in action against Kyle Edmund at the Indian Wells Masters tennis. Like Federer, Nadal has also not lost a single set in the Indian Wells so far.
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Venus Williams advanced to the quarterfinals for the first time since 2001 with a 3-6 6-1 6-3 victory over Shuai Peng, the last remaining qualifier in the draw.
Donald Young upset French 14th seed Lucas Pouille 6-4 1-6 6-3 but Taylor Fritz was knocked out of the tournament by Tunisian Malek Jaziri 6-4 3-6 6-3.
Federer did not feature in second half of the season previous year due to knee problems, but the Swiss ace has been in great form since his return. I try to focus on my next round, and not look beyond that.
But Djokovic said he can not afford to think about a possible quarter-final clash with either of his long-time rivals with 2009 US Open champion del Potro, a 7-6 (7-5), 6-3 victor over fellow Argentinian Federico del Bonis, coming up.
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