World champions in 2005 and 2013, Spain led 18-10 at the half-time mark and never looked back leaving Slovenia to settle for second place in the pool and a potentially tricker second round match.
Spanish goalkeeper Rodrigo Corrales made 12 stops and was named man of the match while Valero Rivera scored six times and David Balaguer collected seven goals.
Spain will next face Brazil for a place in the quarter-finals where they will start as huge favourites.
Brazil managed just fourth place in Group A after losing 28-24 to Russia.
Iceland made the last 16 after drawing 27-27 with Macedonia who were already qualified.
Iceland finished on the same number of points as Tunisia but went through on goal difference.
Tunisia wrapped up their group campaign with a 43-34 win over Angola but were left to regret lost opportunities in earlier 28-28 draws with Slovenia and 22-22 against Iceland.
Next up for Iceland is a clash with defending champions France who finished their Group A campaign with a perfect record thanks to a 28-23 win over Poland.
In the same section, Norway took second place with a 38-23 win over Japan with Bjarte Myrhol hitting seven goals.
Norway will face Macedonia in the next round while Russia will take on Slovenia.
The group stage of the championship concludes on Friday with most attention on the clash between Germany and Croatia with top spot in Group C the reward for the winners.