The home team avoided a shock playoff exit by running out a comfortable winner in Zagreb on Tuesday night.
After a goalless draw in Friday's first leg in Reykjavik, Croatia claimed the ascendancy when Mandzukic produced a composed back post finish in the 27th minute.
The striker was given a straight red card before the break, though, for a crude challenge on Johann Gudmundsson, as Iceland entered halftime with hope.
However, those dreams were dashed just two minutes after the resumption as Srna's first-time strike from just inside the penalty area beat Iceland goalkeeper Hannes Halldorsson from an acute angle.
Iceland, which was hoping to become the nation with the smallest population ever to reach a FIFA World Cup, tired after the second goal and it was only kept in the game by Halldorsson, as its stunning run through qualification came to an end.
Both sides made two changes from the first leg, as Ivica Olic and Mateo Kovacic came in for Croatia, while for the visitors, Birkir Saevarsson and Eidur Gudjohnsen replaced the suspended Olafur Skulason and the injured Kolbeinn Sigthorsson.
Kovacic blasted over from the edge of the area in the first minute, and although Iceland had the ball in the back of the net, Alfred Finnbogason was flagged for offside well before finishing.
A Luka Modric effort – which deflected wide – began a sustained spell of pressure from the hosts, as they had penalty claims for handball against Ari Skulason denied and Srna forced Halldorsson into an excellent save from a free kick.
Mandzukic then gave Croatia the lead, as Ivan Rakitic's ball in from the left was flicked towards goal by Ivan Perisic, with the Bayern Munich forward well placed to stab in from close range.
Olic then wasted a free header, nodding Srna's cross over the crossbar, before Halldorsson had to be alert to keep out an effort that deflected off Skulason and was creeping into the bottom corner.
Mandzukic's red card threatened to turn the match on its head, but Srna eased those fears with his goal just after halftime, as he benefited from a mazy Kovacic run before thrashing an effort home.
Kovacic then embarked on another excellent run but saw his effort saved by the outstretched foot of Halldorsson, before Olic saw his volley from a corner smack the underside of the crossbar.
Perisic was the next to be thwarted by the Iceland goalkeeper when presented with a one-on-one opportunity.
Halldorsson was on top form, and he came to the rescue again to deny Daniel Pranjic with 15 minutes to go, but two goals were enough as Croatia sealed their place in Brazil.