Two-time world champion Lewis edged out Michael Smith in a thrilling contest, which saw Smith squander two darts to win in a dramatic climax to their second round clash.
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Premier League runner-up Smith kicked off each of the last two legs with back-to-back 180s but could only watch as Lewis took out 84 to punish his missed match darts in the deciding leg.
Cross, who won a Players Championship event last weekend to pick up his first title since becoming World Champion, stayed in hunt for another success after winning the last three legs to defeat Steve Beaton.
The world number three trailed 5-3 but managed to salvage the situation and set up a second round clash against Mervyn King, who came back from the same position to defeat German Darts Open winner Max Hopp.
World number one Michael Van Gerwen eased past Scott Taylor 6-2 to book his place in the round three, where he will take on Brendan Dolan, who overturned a 4-1 deficit to defeat John Henderson.
Peter Wright enjoyed a dominant 6-1 success against Barry Lynn who defeated Chris Dobey on Friday, while Mensur Suljovic saw off Ryan Joyce by the same the margin.
World Grand Prix champion Daryl Gurney suffered a rapid exit, losing out to Ricky Evans by six legs to three.
Joe Cullen produced a brilliant performance to see off Friday's top performer Madars Razma. The Yorkshireman averaged 105.99 in a 6-3 success.
Welsh World Cup of Darts teammates Gerwyn Price and Jonny Clayton experienced differing fortunes as Price defeated Jelle Klaasen 6-3 but Clayton missed five match darts before losing out to Darius Labanauskas.
James Wade fended off a spirited performance from 17-year-old Rusty-Jake Rodriguez, taking the last three legs to win 6-4.
Darren Webster defied a 103 average from Spain's Cristo Reyes to edge a thrilling contest 6-5, while Gibraltar Darts Trophy semi-finalist Steve West defeated number nine seed Ian White 6-4.
Simon Whitlock gained revenge for two defeats at the hands of Jermaine Wattimena at last weekend's Players Championship events by defeating the Dutchman 6-3.
Stephen Bunting also claimed a 6-3 success as he won five consecutive legs to beat Peter Jacques.
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