The Australian was 2-0 up after Chen, who had to defeat Fergal O’Brien in a wild card qualification match the previous day to make the first round proper, missed the final green while on the verge of levelling for 1-1.
The Chinese opened his account by taking frame three but Robertson’s 53 break put him in a commanding position heading into the mid-session interval.
Robertson kept his momentum by taking frame five for a 4-1 lead and although a series of miniature breaks from Chen to claim the sixth delayed the inevitable, the 2010 world champion pounced on an unforced error to finish off the 29-year-old.
Next up for Robertson is Joe Perry, who knocked out Matthew Stevens on Monday.
Six-time world champion Steve Davis almost pulled off a stirring comeback after forcing a deciding frame against Ricky Walden from 4-1 down.
However, after failing to take three clear chances to finish the veteran off, Walden finally came good with a 92 break which snatched the contest 5-4.
Davis, who dominated the sport in the 1980s, gave an early indication of his resolve when bouncing back to level the second frame 70-70 and force a re-spotted black, which he sunk for 1-1.
Walden took control with three on the spin and appeared set to coast into the last-16 only for ‘The Nugget’ to pull one back with a 49 break when the Chester resident let him back on the table.
The formula repeated twice more as Walden lost his way after a pair of runs in the 30s and found himself level.
But the winner of this very event four years ago managed to avoid repeating his mistakes in the final frame, powering to a 92 break and though he was denied a possible century by the final red, a second round match with Mark Williams was finally secured.
Stephen Lee defeated Marcus Campbell 5-3 after the two had exchanged the advantage in a defensive battle over six frames until Lee exerted control over his opponent to claim the final two.
Lee’s next challenge comes in the form of 2006 world champion Graeme Dott, who defeated qualifier Jin Long.
And Stuart Bingham shook off a slow start to take another final-frame nail biter 5-4 against Tom Ford.
A 70 break followed by two mini-runs of 39 and 44 brought Bingham level at 2-2 after Ford comfortably moved ahead early on before runs of 71 and 57 made it four straight frames.
Ford racked up a 42 and a 47 as he showed his own fighting spirit to take the encounter to the wire, but another half-century from Bingham set him on his way to secure a last-16 meeting with Jamie Cope, who progressed at the expense of defending champion and world number one Mark Selby.