Zlatko Dalic’s side came into the contest knowing they merely had to match the result of Wales to seal automatic qualification, but an early Neco Williams goal against Turkey in Cardiff put the hosts under immediate pressure.
Despite slipping down to third in the table, Croatia would have been encouraged by their dominant start. Ognjen Cancarevic made a superb save to keep out Andrej Kramaric's fierce strike, while the Armenia shot-stopper was called into action again to save Marcelo Brozovic's header.
The hosts were dictating the play in search of a goal that would move them back into the top two, but further clear-cut opportunities were proving hard to come by against a resolute Armenian defence.
The visitors nearly stunned the Zagreb crowd when Kamo Hovhannisyan surged into the box, and Dominik Livakovic did brilliantly to tip the Astana defender's effort over the bar. This seemed to spark the hosts into action, as Luka Ivanusec's first-time strike went a whisker wide of the target.
There was a palpable sense of relief around the ground when Budimir broke the deadlock in the 43rd minute, as the Osasuna forward powered home a header from Borna Sosa’s cross to propel Dalic’s men to the top of Group D before the break.
Croatia were eager to kill off the game as soon as possible, knowing that an Armenia equaliser would send them plummeting back down into third. Luka Modric was pulling the strings brilliantly in midfield, and was the instigator of everything positive going forward for the hosts.
Cancarevic was called into action again to deny Josko Gvardiol, while Budimir could not add to his tally after skewing his effort wide of the post.
The Kockasti were still pressing for a second, and Canacrevic kept the deficit at one with another superb stop to parry away Brozovic's strike.
In the end, Croatia were forced to settle for one goal which secured second spot in the group and a 13th major tournament appearance. It was a spirited performance from Oleksandr Petrakov’s visitors, but they are now winless in their last six matches across all competitions.
Flashscore Man of the Match: Luka Modric (Croatia)
Greece hold France to draw in four-goal thriller
Neither Greece nor France had anything to play for in their clash in Athens, with the hosts already certain to head to the play-offs and the visitors already certain to top the group, but that didn't stop the two sides from putting on a show.
After going 1-0 down to an opener from Randal Kolo Muani, the Greeks rallied and turned the game on its head with two goals in five minutes around the hour mark.
France responded through Youssouf Fofana with just over 15 minutes to go, and neither nation could find a winner after that.
Monday's other qualifiers:
Group B
Group D
Group I
