Lincoln's dismal form in front of goal continued as they failed to find the net for the fourth consecutive game.
Manager Keith Alexander tried out yet another new strike partnership but his team struggled to create chances.
Newly-promoted Doncaster at times looked set to sweep them aside with their powerful attacking game, but somehow Lincoln held out mainly thanks to some poor finishing from Rovers front man Leo Fortune-West.
Afterwards Doncaster manager David Penney said: "We had our chances, especially in the second half but didn't put them away.
"In the end we're disappointed that we haven't got three points. We just have to work harder on our finishing." Doncaster almost took the lead after five minutes when they broke quickly and Gregg Blundell provided an excellent cross for Paul Green to head towards the top corner.
It looked a goal all the way but somehow Lincoln keeper Alan Marriott managed to keep it out with a point-blank save.
Blundell then headed over the bar from ten yards before midfielder John Doolan wasted another opening when he volleyed wide from the edge of the box.
Three minutes into the second half Marriott produced a superb diving save to keep out a free kick from winger Michael McIndoe.
Fortune-West spurned two more chances before Lincoln finally started to move forward on the hour. They almost snatched the lead in the 62nd minute when defender Mark Bailey floated in a free kick only for Andy Warrington to pull off a diving save.
Lincoln were left hanging on with Marriott twice making late saves to prevent Simon Marples finding the net.
Lincoln manager Keith Alexander said: "At least we have a point on the board and we have made a start.
"Doncaster impressed everyone, they played some decent football and put us under a lot of pressure but we kept a clean sheet.
"They're a strong team and had won three out of three before today. You can't be disappointed when you take a point off good sides like them."