But they maintained their unbeaten record away from home and the point gained kept them at the head of the table.
Tranmere created the better chances in the first half but Forest finished much the stronger side in a game in which defences always dominated.
Skipper Ian Goodison was superb in the heart of the rearguard and Julian Bennett produced a five-star display in the left-back berth for the visitors.
Chris Shuker brought an excellent save from Forest's Paul Smith with a 20-yard free-kick on the half hour.
Then Smith was at his best again two minutes later when punching away another free-kick this time from 25 yards by Kevin Ellison.
Gareth Taylor was out of luck with two headers against his former club - the second of which just before the break shaved the outside of the post.
Neil Harris missed the target with an early header for the visitors and then in the 16th minute he saw a fine angled shot turned aside by Tranmere keeper Gavin Ward .
Ellison missed an excellent chance to break the deadlock on 57 minutes when blasting over from eight yards. He also saw a header following a corner blocked out in a crowded goalmouth.
Forest used substitutes Kris Commons and Grant Holt for the last half an hour and certainly looked the more likely side to snatch the victory.
Commons saw a drive saved and then volleyed over, while Ward did well to tip over a Grant Holt header in the 87th minute.
Then in injury time he was on hand to push away a long-range effort by Wes Morgan.
But luck was on his side just before the close when a header from Forest skipper Ian Breckin was deflected on to the bar.