The result leaves Wales with four points from two games while Bosnia have one and plenty of work to do after losing their opening game 2-1 to Cyprus at home last month.
Welsh forward Gareth Bale and Bosnia and Manchester City striker Edin Dzeko both had a quiet games as their markers gave them preciously little room to operate on a slippery surface, with the visitors creating more chances.
Despite that Real Madrid Bale had a fierce angled shot tipped away for a corner by Asmir Begovic in the dying moments to deny Wales victory.
Chris Coleman, the Wales manager said: “The performance pleased me more than the point.
“The crowd were incredible, the atmosphere reminded me of when I was a player and we took on teams at Cardiff Arms Park. We rode our luck a little, but so did they. The players were magnificent, I was so proud of them. Lads were throwing their heads in front of shots and we need to have that mentality.”
A high-tempo first half, in which Hennessey kept out a bouncing Miralem Pjanic shot from long range, was followed by an even more eventful second period as the 27-year old Crystal Palace 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 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-odd yards after the Real Madrid winger weaved his way past two markers on the left flank. It would have been a stunning end to an enthralling fixture.
“It is a good point, it would have been nice to get all three but I think we have shown how much we have grown tonight,” said Williams afterwards. “I should have scored. We had a few chances, I had two and I am kicking myself about it.”
Ahead of Monday’s home fixture against Cyprus, the captain added: “If we can get seven points from our first three games, that would be a nice return.”
Hennessey, who picked up the man of the match award at full-time, said: “All the lads produced a great performance. We always knew that Bosnia are good team, they have great strengths but the lads did well.”
Wales: Hennessey, Gunter, Chester, A Williams, Davies, N Taylor, King, J Williams (G Williams 82), Ledley, Bale, Church (Robson-Kanu 65). Subs not used: F Williams, D Edwards, Cotterill, Gabbidon, Ricketts, Lawrence, G Edwards, J Taylor, Letheren.
Bosnia-Herz: Begovic, Hadzic, Sunjic, Mujdza, Besic, Lulic, Susic, Medunjanin, Ibisevic (Hajrovic 83), Pjanic, Dzeko. Subs not used: Fejzic, Vrsajevic, Vranjes, Cimirot, Prcic, Visca, Kvesic, Dujkovic.