Robert Page’s side looked set to start the post-Gareth Bale era with defeat to Croatia after Andrej Kramaric’s first-half strike.
But supersub Broadhead tapped home at the far post after Chris Mepham flicked on Connor Roberts’ long throw.
It sparked wild celebrations among the 1,800 travelling Welsh support in Split.
This Group D opener was always going to be a daunting task for the Dragons with or without Bale, who retired in January, and so it proved for long parts as Luka Modric and co showed their class.
But Wales, led by new captain Aaron Ramsey, refused to give up and gained a late leveller with just 40 seconds left on the clock.
Boss Page said pre-match he wanted to at least see a performance following a disappointing group stage exit in Qatar – and although it was tough, he got a result.
And, despite the Dragons being dominated for large parts, the visitors will also rue Dan James’ second half sitter on their way home from the Balkans.
The point will give Wales major hope of reaching a third successive Euros finals and a fourth major tournament in their last five attempts.
This was dubbed as a new era post-Bale but Wales started with eight of the side that lost 3-0 to England which sent them packing from the World Cup.
Wales lined up in a 4-2-3-1 formation with new skipper Ramsey given the licence to support lone striker Kieffer Moore.
Croatia, ranked seventh in the world, had never lost a home qualifier and their only defeat from their last 14 matches came in the World Cup, where they were beaten by Lionel Messi’s eventual winners Argentina.
The hosts bossed it from the off.
Page, who was fuming with Nottingham Forest for their handling of Brennan Johnson’s groin injury to make him unavailable for international duty, was also gutted that Luka Modric had not called it a day after Qatar.
And Real Madrid playmaker Modric, 37, who was winning his 163rd international cap, forced Danny Ward to turn a fizzing 25-yard shot around his post in the third minute.
That came from Connor Roberts conceding possession and the Burnley full-back was in trouble moments later.
Roberts was second best in a challenge with Ivan Perisic and the Tottenham star saw his dangerous cross evade Marko Livaja and hit Joe Rodon but luckily the ball flew away for a corner.
Wales failed to keep hold of the ball, allowing Croatia to pile on the early pressure.
Keeper Ward, dropped by Leicester boss Brendan Rodgers for Daniel Iversen last weekend, showed fine flexes to deny Hoffenheim’s Kramaric after a classy touch by Mateo Kovacic.
Ethan Ampadu was booked for pulling back Modric and Perisic thought he had put Croatia ahead from the resulting free-kick.
But Portuguese referee Joao Pinheiro ruled Livaja had fouled Roberts in the build-up before Perisic’s strike was deflected in by Chris Mepham.
Wales had not heeded the warning and Page’s men fell behind in soft fashion on 28 minutes.
Rodon lost an aerial battle with Livaja and then Kramaric burst through a weak challenge from Neco Williams.
As the attack developed, Mepham dropped off and that opened the space for former Leicester striker Kramaric to fire home from the edge of the area.
It had been coming.
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Modric, in delightful form, volleyed wide from a Perisic knockdown before Sosa shot tamely.
Wales had been dominated and the 1,800 travelling fans had to wait until three minutes before half-time for a first effort at goal.
Josko Gvardiol fouled Harry Wilson and the Fulham winger saw his dipping effort, in trademark Bale territory, fly over the crossbar.
Kramaric shot wildly over the bar after Williams gave up possession.
In truth, Croatia, with 70 per cent of the possession in their favour and nine shots to Wales’ one, would have been frustrated they were only one goal up on their return to the dressing rooms at the break.
Chelsea midfield ace Kovacic missed a golden chance to put the hosts two goals clear when he skied over from close range after a slick one-two with Kramaric.
Yet for all Croatia’s dominance, Wales could have levelled on the hour mark.
Wilson edged a battle with Gvardiol, Ramsey recycled and Wilson’s diagonal pass found James unmarked but the winger miscued a volley wide.
Just as Wales finally looked to pose a threat, Page surprisingly made a triple substitution, withdrawing Ramsey, Wilson and James for Sorba Thomas, Wes Burns and Broadhead of Ipswich.
But, after Perisic smacked the bar with a volley, Broadhead came up trumps to bag an unlikely draw.