Littler, who would usurp Luke Humphries at the top of the standings if he reaches the final in Wolverhampton, took a 5-0 lead before his Dutch opponent got on the scoreboard.
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Nijman reduced his deficit to 6-3 but, after missing three darts on a double to get two legs back, found himself 7-3 down.
World champion Littler won 10-4, finishing with an average of 105.38, and will play Josh Rock in the quarterfinals.
“I’ve got my eyes on everything,” Littler told Sky Sports. “The title, number one in the world; if I reach the final, I will be number one in the world, but we have to go game by game.”
Three-time champion Van Gerwen faced his compatriot Danny Noppert and both finished with 170 checkouts in the first and third respectively in a fast start.
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Van Gerwen was in pursuit for most of the match and stayed within range before his compatriot made it three in a row to take a 9-5 lead before winning 10-6.
Rock, who won the World Cup of Darts for Northern Ireland alongside Daryl Gurney in June, held off Connor Scutt to claim a narrow 10-9 victory.
Rock held leads of 3-0 and 8-5, but Scutt fought back to force a decider, which the Irishman, with the shot, took advantage of to advance to the quarterfinals.
In an all-German match, Lukas Wenig overcame a close match against Niko Springer to win 10-8.
Thursday results
Lukas Wenig 10-8 Niko Springer
Josh Rock 10-9 Connor Scutt
Luke Littler 10-4 Wessel Nijman
Danny Noppert 10-6 Michael van Gerwen