Not even monsoon-like conditions could deter the Irish producing what King branded the best performance of the campaign on the road.
Montenegro blew their chance to torpedo Ireland’s hopes and they stay deadlocked on eight points each.
“After such a magnificent performance from the lads tonight, we’ll be very confident of beating them next time out at home,” King said.
“Montenegro have a game in hand but that will be taken care of once we do the business at home and put the ball in the net. Failing to do that here spoiled what was an otherwise excellent effort by the lads.”
Ireland looked the brighter of the two qualification contenders from the outset. This despite the heavy downpour throughout the first half threatening to compromise their preferred passing style.
Sean Murray and Jack Grealish linked well to expose a lack of pace in the heart of the Montenegro defence, with Murray and Anthony Forde both testing Petkovic before the break.
Ireland, relatively untroubled in the first half, were given a scare four minutes after the restart when Stefan Mugoša wriggled free to head beyond Sean McDermott only for Samir Carruthers to clear off the line.
Though Sean McDermott in the Irish goal became busier as the game wore on, Ireland ended the stronger.
With 10 minutes left, O’Brien’s knock down fell perfectly for the onrushing Callum Reilly, but the Birmingham City midfielder blazed over.
Then, moments later, Grealish almost forced a winner in the last minute with a near post shot that was turned around the post before O’Brien missed the sitter.
MONTENEGRO: D Petkovic: N Gojacanin (V Jovovic 69), E Alic, R Radunovic, M Bakrac; N Kosovic, B Jankovic; M Vukcevic, D Zoric (A Kaludjerovic 69), L Ðjordevic; S Mugoša (I Pejakovic 79).
REP OF IRELAND: S McDermott (Sandnes Ulf); M Harriman (Gillingham), S Duffy (Yeovil Town), D Williams (Bristol City), S McGinty (Sheffield Utd); C Reilly (Birmingham City), S Carruthers (MK Dons); A Forde (Wolves), S Murray (Watford), J Grealish (Notts County); A O’Brien (Millwall).
Referee: Vladimir Vnak (SVK).