City looked nervous throughout the game as they knew that a win would take them into the Championship regardless of other results.
City started slowly and it was Alan Dunne who had the first chance for Millwall when he fired a vicious shot from 20 yards which was fumbled by keeper Adriano Basso.
Luckily for City, Liam Fontaine was on hand to clear from danger.
The first half failed to kick into life with both sides struggling to create any clear-cut chances.
And it wasn't until the 25th minute until City registered their first chance when David Noble pulled his shot wide from 20 yards.
The best chance of the half fell to the in-form Darren Byfield, who was one-on-one with Basso but the Brazilian keeper came out on top by pushing his shot to safety.
City came out of the traps the faster in the second half and had a chance to take an early lead when Noble's curling shot from the edge of the area went just over the bar.
Neil Harris then blasted over from close range for Millwall after a Ryan Smith cross just after the hour mark.
Millwall keeper Lenny Pidgeley was then called into action to deny Jamie McCombe's downward header after a Lee Johnson free-kick.
But with 12 minutes remaining, Millwall skipper Robinson popped up at the far post and volleyed home a Harris cross from six yards.
The result means that Bristol City will have to beat already relegated Rotherham on the final day of the season to ensure promotion.