Robert Snodgrass forced Tim Howard into a fine save in the second half, while substitute Aron Johannsson was thwarted by a brilliant David Marshall save in the last 10 minutes at Hampden Park.
The result means Scotland are undefeated in three games for the first time since September 2011.
Jurgen Klinsmann left out the likes of Clint Dempsey and Landon Donovan, who are involved in the MLS play-offs, and Scotland controlled the opening exchanges, with Steven Fletcher heading over a Snodgrass cross.
But America have scored 16 goals in their last four friendlies and always carried a threat. Sunderland striker Altidore had an early sight of goal but fired over from 20 yards.
Fletcher was brought down on the edge of the area by Omar Gonzalez after 23 minutes, which gave Charlie Mulgrew a very presentable shooting opportunity but his curling effort sailed over.
The home side continued to look dangerous and should have scored after 34 minutes when Fletcher fed Craig Conway on the left but with just the goalkeeper to beat, he elected to go near post and slotted wide.
The first shot on target for either side arrived in the second minute of the second half when Sacha Kljestan and Altidore linked up before the latter shot straight at Marshall.
Scotland forced Howard into a fine save after 52 minutes when Steven Whittaker's marauding run was ended 30 yards out by Geoff Cameron's foul and Snodgrass curled a beautiful free-kick over the wall that the Everton goalkeeper did well to tip over on his 95th appearance for his country.
Altidore was inches away from putting the visitors on the way to their 17th victory this year after 58 minutes when Cameron intercepted a poor Mulgrew touch and fed the striker but his rasping drive went just wide with Marshall well beaten.
The USA showed the form late on that helped them win 12 consecutive wins earlier this year. Grant Hanley failed to clear inside his own area after 82 minutes and Johannsson forced Marshall into a smart low save before Hanley made amends by making a crucial intervention with Altidore waiting for a tap-in.
A minute later, substitute Brek Shea broke down the left and fed Johannson, who made space in the box but skewed wide as the game ended 0-0.
