The Spanish defender's close-range header on 64 minutes was followed by Gregory Tade's 15-yard shot through a crowded area five minutes later to double the lead.
Substitute Rory Fallon's 76th-minute goal put the visitors back in it, but they failed to find an equaliser.
The win reduced the gap between the clubs to just two points and took the Highlanders further from the foot of the SPL.
Caley Thistle's top scorer Andrew Shinnie and defender Ross Tokely were both sidelined by injuries following last week's 2-1 loss at Rangers.
Defender Thomas Piermayr returned from a back injury while David Davis was also in for the hosts after serving a suspension.
The Dons made four changes to the side which beat Hibernian 1-0 last time out.
Youl Mawene, Andrew Considine, Chris Clark and Josh Magennis came in, while Rory McArdle, Rory Fallon and Fraser Fyvie dropped to the bench and Mohamed Chalali missed out.
There was little festive goodwill in the opening moments when Golobart picked up a yellow card for a challenge on Scott Vernon.
Richie Foran showed the home side's attacking intent with a diving header just wide from inside the box after a Jonny Hayes' free-kick.
Kari Arnason then powered a header wide from Robert Milson's corner before Vernon headed wide after connecting with an Arnason throw-in.
Jason Brown was equal to a low shot from outside the area by Hayes before, at the other end, Inverness goalkeeper Ryan Esson was forced into the first save of the game when he parried a Magennis shot wide.
Graeme Shinnie tried his luck from 40 yards with the wind behind him but his effort floated over the bar.
Magennis made Esson work again with a close-range shot which hit the goalkeeper and spun out for a corner.
Milson's cross-cum-shot was the best of the opening stages of the second period, but it was just off target.
Davis, who showed glimpses of the quality he possesses as a loanee from Premier League side Wolves, powered in a low, angled effort which Brown turned away for a corner.
Hayes took the resulting set piece to find on-loan Wigan teenager Golobart, who sent home a powerful header to open the scoring on 64 minutes.
Billy McKay shot over as Inverness continued in the ascendancy and their pressure paid dividends when Gregory Tade's low shot found the net through a crowded penalty area in 69 minutes from 15 yards, following a Hayes corner.
Hayes was next to test Brown with a low shot from 30 yards before Fallon pulled one back for Aberdeen on 76 minutes.
Six minutes after coming on as a substitute, Fallon's low shot from six yards beat Esson after he was picked out by Milson.
Milson himself sent a good chance over as Aberdeen looked for an equaliser, while substitute Greg Tansey almost extended his side's lead in stoppage time as Inverness held on for their first home win since October 1.