The world champions dominated the majority of the game in Malabo on Saturday but were wasteful in front of goal, with substitute Fernando Llorente particularly guilty.
Andoni Goikoetxea's charges briefly threatened a shock draw when Jimmy Bermudez cancelled out Arsenal midfielder Cazorla's opener, but Juanfran's winner spared Spain's blushes.
Spain produced the best openings of the first half and Jesus Navas' lob almost put the visitors ahead efore Cazorla capitalised on a mistake from Danilo.
Equatorial Guinea equalised through Bermudez's header, but the sides were level for just seven minutes as Juanfran thrashed home from close range.
Spain had several opportunities to increase the lead and Llorente thought he had added a third, only for Andres Iniesta to be ruled offside in the build-up.
Vicente del Bosque took the opportunity to rest several of his star players and handed a debut to Marc Bartra, while Ivan Bolado was given the role as Equatorial Guinea's lone striker.
The visitors dominated first-half possession and were nearly ahead as early as the seventh minute when Navas' inventive chip almost dipped over Danilo.
Spain were duly rewarded for their pressure six minutes later, when Danilo dropped a straight-forward cross from Juan Mata and Cazorla profiting from the gaffe as he tapped into the empty net.
Equatorial Guinea had their first sight of goal after 35 minutes when Rodolfo Bodipo met Javier Balboa's centre, but his strike was deflected over the crossbar.
And from the resulting corner the home fans were sent into delirium when Bermudez levelled by rising highest to head home Juvenal Edjogo's delivery.
However, their joy was short-lived as three minutes before the break Cazorla's cross deflected into the path of Juanfran and he rifled home from close range.
Llorente was introduced as a second-half substitute and will feel he could have done better after 54 minutes when he shot tamely at Danilo from Navas' cushioned header.
The Juventus striker did have the ball in the back of the net on the hour-mark when he tapped home Iniesta's centre, but the Barcelona midfielder was harshly adjudged to be offside in the build-up.
Spain's dominance continued and Llorente missed another clear opportunity with a weak back-post header from Navas' deft cross with 20 minutes remaining.
Several substitutions in the close stages stemmed the flow of the match, as Spain comfortably saw out the victory.
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