He won the first session of his match against Xiao Guodong 6-2 and shared the evening’s eight frames to maintain the advantage in the best-of-25 contest.
However, it could have been worse for his Chinese opponent, who won the last two frames to trail 10-6.
Elsewhere, there was little to choose between world No 8 Marco Fu and his opponent Neil Robertson, currently ranked one place below in the rankings – the winner facing either Selby or Xiao.
Fu hit back from 4-1 down to head into the evening session against the Australian locked at 4-4, with a 118 the start of his recovery – and the first two frames of the evening were shared.
The Hong Kong player then took the lead for the first time in the contest when a break of 72 helped him to win the 13th - but the see-saw nature of the contest was to continue.
Robertson won the next two to regain the lead, only for Fu to land the 16th and ensure the pair were level again, at 8-8.
Earlier, Stephen Maguire ended Rory McLeod’s hopes of further progress with a session to spare.
Maguire beat McLeod, the first-round conqueror of pre-tournament favourite Judd Trump, 13-3 to reach his fifth Crucible quarter-final – his first since 2012.
A break of 119 in the ninth frame was the highlight for Maguire, who will face Barry Hawkins or Graeme Dott for a place in the last four.
Hawkins, on his 38th birthday, was in impressive form early in the evening, turning a 5-3 advantage into a 9-3 lead against the 2006 champion.
Scot Dott then won three successive frames to reduce the deficit to 9-6 and keep alive his hopes of progressing - with a 105 clearance in the 15th the highlight.
However, Hawkins took a nervy final frame to lead by four.
Ding Junhui won the battle of the Chinese players with a tense 13-12 victory over Liang Wenbo to set up a quarter-final meeting with O’Sullivan.
But Ding had to fight all the way after surrendering a two-frame lead to trail 10-9 to Liang, who took the first three frames of the session with breaks of 58, 98 and 61.
On Saturday, Ding took the 20th frame before a break of 85 saw Liang win the next to go in front once more. A break of 80 helped Ding level again at 11-11.
When Liang won the next he looked set for the win but a fine 132 from Ding took the match into a decider which the latter won with a break of 70.
O’Sullivan beat Stephen Murphy 13-7 earlier in the day.