But the great start was followed by two straight losses: 3-2 to England in Spain's first home defeat in 15 years, and 3-2 at Croatia on Thursday after conceding in stoppage time.
Ivan Rakitic has been sent back to Barcelona after suffering a hamstring in the second half of the win over Spain - so Chelsea's Mateo Kovacic is set to come into the line-up.
But Jedvaj's late victor now means victory at Wembley over England, who they beat 2-1 in the World Cup semifinals, would put them in the final phase.
Respect was a hot topic between the sides around the World Cup semi-final, with Croatia complaining England had taken victory for granted, but Rakitic knows what to expect when his side face the Three Lions again.
'I'm more anxious about our team because we played against Spain two days ago.
"We've added more depth to the squad, in terms of some more young players emerging, more competition for places".
"We have the solutions and we go to Wembley to enjoy the football".
"We're trying to break barriers down and play in a different way, a different style and we're getting better all the time so we're looking forward to the challenge tomorrow". If we play our best like we did against Spain I think we can win the match'. England can avoid relegation with a draw or three points. So it's not that we wanted to show any disrespect to England but it is just in that moment all Croatians wanted to embrace all other Croatians! At Barca there are plays that are rehearsed and trained and I could see that England also had those plays very well-worked. "With a little bit of luck we got the second goal with a headed clearance that falls right to Mario Mandzukic".