The result left Wales with four points from two games after beating art while Bosnia have one and plenty of work to do after losing their opening game 2-1 to Cyprus at home last month.
Wales coach Chris Coleman praised his men for what he called a "heroic" performance when he spoke to Sky Sports afterwards.
"I think the performance pleased me more than the point. Our supporters were fantastic, the atmosphere was fantastic and the lads stepped up.
"We knew we would have to ride our luck a little bit, but my lads were magnificent, its the proudest I have been. To a man -- they were heroic almost."
"DIFFICULT MATCH"
Bosnia coach Safet Susic told BHT TV: "It was a very difficult match in which both teams missed a lot of chances, but we had more.
"Wales are a good team with Bale as their outstanding player who needs only a bit of room to do a lot of damage. We were a bit impatient at times but I am not unhappy with the result.
"However, we are now under pressure to beat Belgium on Monday and we will need a bit of luck."
Welsh forward Gareth Bale and Bosnia striker Edin Dzeko both had a quiet game as their markers gave them preciously little room to operate on a slippery surface, with the visitors creating more chances.
Despite that Bale had a fierce angled shot tipped away for a corner by Asmir Begovic in the dying moments to deny Wales victory.
A high-tempo first half, in which Hennessey, named as man of the match afterwards, kept out a bouncing Miralem Pjanic shot from 25 metres, was followed by an even more eventful second period as the 27-year-old keeper produced a string of good saves.
He twice denied midfielder Haris Medunjanin and also palmed away a cheeky Dzeko header in a frantic 15-minute spell as the Bosnians, roared on by 3,000 noisy away fans, pressed forward after the interval.
Wales missed their best chance when captain Ashley Williams headed over the bar with the goal at his mercy in the 77th minute after Bale delivered a teasing cross from the left.
Hennessey again rescued the Welsh when he tipped over a viciously swerving free kick by Pjanic as the home team held off the more adventurous Bosnians in the closing stages.
Wales nearly grabbed a late winner when Begovic somehow clawed out an arrowed Bale scorcher from 20 metres after the Real Madrid winger weaved his way past two markers on the left flank.
Wales only appearance in a major finals was in the 1958 World Cup in Sweden but they have a chance to make it to the expanded 24-team European championship in France in 2016 and victory over Cyprus on Monday will leave them with a creditable seven points from their opening three matches.
(Writing by Zoran Milosavljevic in Belgrade, edited by Mike Collett)
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