The 2002 champion ground out a 13-9 win over left-hander King and will face either Shaun Murphy or Ali Carter in the last eight at the Crucible.
Ebdon began the evening session with a 9-6 lead and quickly extended that to 11-6 with consecutive breaks of 79.
King battled back to take the next two frames with the help of a break of 121 before Ebdon edged closer to the winning line by winning a scrappy 20th frame.
King, a surprise winner over last year’s runner-up Mark Selby in the first round, produced a break of 79 to stay alive but Ebdon’s run of 54 in the next ultimately proved enough to seal victory.
Ebdon had led 5-3 going into yesterday’s first session, and took the opening frame with a break of 73 but King snatched the next 67-66 after Ebdon had been first in with a run of 52.
2002 world champion Ebdon then took the next two frames to lead 8-4 before King, who knocked out last year’s runner-up Mark Selby in the first round, took a scrappy 13th frame to reduce the deficit.
The next two frames were shared to leave Ebdon 9-6 ahead, and he went on to edge out a gritty victory.
John Higgins resumes this morning against Ryan Day (10am) after a day when he showed he was feeling the pressure of trying to retain his World Championship crown.
Higgins squandered a promising position against Welshman Day. Higgins, looking to become only the third back-to-back winner at the Crucible, led 5-3 overnight and quickly extended his advantage to three frames this afternoon in the last 16 clash.
But the 32-year-old then lost the next three frames in a row, punching the table in frustration after the 11th frame and then flinging the white down the table after being pegged back to 6-6.
Higgins’ mood was not improved by Day taking the 13th frame with a break of 51 to lead for the first time in the match. But the Scot finally rediscovered his touch to take the next two frames with breaks of 99 and 54 to edge back into the lead.
However, Day was looking a far better player than the one who trailed 4-0 in Thursday’s opening session and a run of 93 ensured the 28-year-old ended the day level at 8-8 ahead of this morning’s decisive session.
Rotherham’s Shaun Murphy, winner in 2005, could no doubt sympathise with Higgins after finding himself 6-2 down to Ali Carter after the opening session of their second round match.
Murphy had reached the semi-final or better in six of his last seven tournaments and beat Dave Harold 10-3 in the opening round, but was completely out of sorts against Carter.
The 25-year-old managed just one break above 50 in the session while Carter enjoyed runs of 97 and 100 to take a surprise lead. That match also resumes at 10am this morning.
Ding Junhui trails Stephen Hendry 11-5. That game resumes at 2.30pm tomorrow.
Hendry raced into a 6-2 lead making a flying start with a break of 124 in the opening frame against Chinese superstar Ding, who spent most of the frame with his head down and eyes closed.
Ding took the next frame to level the scores but a break of 61 gave Hendry the third frame and the Scot then took a scrappy fourth as well to lead 3-1 at the mid-session interval.
Ding was enduring a torrid time and had managed a high break of just 26 in those opening seven frames, and it was vital for the Sheffield-based 21-year-old to win the final frame of the session.
In the second session Ding continued to struggle and finished the session six frames in arrears with Hendry needing to win a further two to go through to the quarter-final.