Lewis, who won the title in 2011 and 2012, squandered two match darts at double 20 before losing 5-4 at Alexandra Palace.
The Englishman was continually forced to come from behind, because Van Gerwen was first to the oche in the odd-numbered sets and the opening eight sets went with throw.
Lewis, who averaged 100.8 and recorded 11 maximums, finally edged ahead in the deciding set, breaking his opponent's throw to leave himself just one leg away from victory.
However, he failed to check out on 60, allowing Van Gerwen to mop up 83 with minimal fuss.
The Dutchman, who averaged 103.72 and hit 15 180s, punished Lewis for his misses by winning the next two legs to secure his place in the semi-finals.
Newton raced out of the blocks and claimed the opening two sets, but Wade responded in style to storm into 4-2 lead.
However, Newton was far from finished and he won the seventh set 3-0 before levelling the match at 4-4 to force a decider.
Wade was well below his best and ended with a modest 92.89 average, however he made the crucial breakthrough when it mattered.
The Machine broke Newton's throw at the first attempt in the decider before going on to seal the final set 3-1.