This clash was billed as 'Redemption' by the Scotland camp in the build-up and they ensured the feel-good factor and momentum from recent displays and results under Gordon Strachan continued.
Steven Fletcher was tasked with leading the line, as he made his first appearance for the national team since March after recovering from injury.
The Sunderland forward tried his luck early on with a shot from distance that failed to trouble Tim Howard in the United States goal.
Barry Bannan then collected a neat pass from Alan Hutton and sent a tempting ball into the goalmouth, which was cleared as far as Conway who blasted over.
A period of possession by the Americans followed and Jozy Altidore unleashed a half-volley that he was unable to keep on target.
Scotland had another chance to pile on the pressure when Fletcher was fouled by Omar Gonzalez just outside the box.
Charlie Mulgrew stepped up for the resultant free-kick and sent a curling effort dipping just over the crossbar.
The best chance so far came 10 minutes before the break when Robert Snodgrass slipped a pass through to Fletcher, who teed up the shot for Conway.
The Brighton winger raced into the box from the left and should have opened the scoring but managed to rifle past the upright instead to the disbelief of the home crowd, as the first half ended goalless.
Altidore tested David Marshall shortly after the restart with an angled drive that was comfortably blocked by the Scotland goalkeeper, who was again deputising for the injured Allan McGregor.
At the other end, Conway was brought down by Brad Evans and Bannan played the free-kick square to Mulgrew but his shot was held by Howard.
Snodgrass then produced a superb set-piece - after Steven Whittaker was felled - that forced an impressive save from the USA keeper as he pushed the effort wide.
Scotland continued to press for the opener and claimed for a penalty when Conway's cross appeared to come off the hand of Gonzalez but there was no spot-kick award from referee Michael Oliver.
There was concern for the home side - and for Celtic - when Mulgrew required treatment following a challenge from Mikkel Diskerud but he was able to continue to the relief of club and country.
As the game entered the final 10 minutes, there was a scare for Scotland when Greer's attempted clearance fell for Aron Johannsson and he was denied at close-range by Marshall, before Grant Hanley cleared the danger with Altidore loitering with intent.
Johannsson then passed up another great chance when he met Brek Shea's cutback and sent his effort flashing across goal and past the post as the match ended all square.
|0||1st Half Goals||0|
|1||Shots on Target||2|
|9||Shots off Target||4|
|38.9||1st Half Poss.||61.1|
|49.6||2nd Half Poss.||50.4|