Northern Ireland's Rea finished second after an exciting duel with Welshman Davies at the Spanish circuit.
Rea led for most of the race after starting ninth on the grid and briefly hit the front again on the last lap.
Despite not winning for the first time this year, Rea has extended his championship lead to 50 points.
Marco Melandri of Italy was third with England's Tom Sykes in fourth place.
Davies crashed in Saturday's race one while leading in the closing stages, and the victory sees him regain second place in the overall standings.
Rea, 30, is attempting to become the first rider to win three successive WSB titles.
"I tried my hardest but it wasn't enough," said Rea.
"I had a good first few laps and got stuck into a rhythm but, with the slipstream, the group stayed together.
"It was so windy, it was quite scary.
"On the last lap, Chaz made a mistake and opened the door but then he quickly closed it again.
"Congratulations to Chaz - he did a good job after what happened yesterday."
Rea started the season with double wins at Phillip Island and Thailand, and made it five out of five by winning the first race at Aragon.

BBC Home Affairs Correspondent Vincent Kearney said it is possible the weapon was an AK47, which has previously been used in dissident republican attacks.
Up to eight shots struck the passenger side of the car parked at Rossnareen Avenue, at about 18:50 GMT on Thursday.
Two male officers who were in the car were not injured but were said to have been badly shaken.
Police described it as a "mindless, reckless attempt to kill officers". Dissident republicans are being blamed.
Ch Supt Nigel Grimshaw said the police car's armour-plating and bullet-proof glass had stopped the officers from being seriously injured or killed.
Detectives believe the attackers made off in a BMW car that had been waiting nearby at Tullagh Park.
The car, which was fitted with a false Republic of Ireland registration plate, was later found abandoned and on fire at Cluain Mor Drive in the Beechmount area.
Police described the gun used in the attack as "accurate firing".
One of the officers was looking through the passenger window when it was struck by two bullets.

The 18-year-old, who can play as a striker or winger, spent the first half of the campaign on loan with Town's League One rivals Oxford United.
Oxford were keen to extend the deal for the entire season, but the Wales Under-19 international has opted instead to move to Shropshire.
He has scored twice for Oxford this term, both in knockout competitions.
Roberts, who has made 14 substitute appearances in League One this season, made his Albion debut as a 17-year-old on the final day of last season as a 73rd-minute substitute in the 1-1 home draw with Liverpool.
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Defending champion Jonathan Rea's run of five successive World Superbike victories ended when Chaz Davies won race two at Aragon on Sunday.
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A military assault rifle was used in an attack on a police patrol car in west Belfast.
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Shrewsbury Town have signed West Bromwich Albion teenager Tyler Roberts on loan for the rest of the season.