The Dons had failed to find the back of the net in their first four matches of the new SPL campaign but it took them only 12 minutes to take the lead, Milsom slotting home after fine play by Josh Magennis.
The home side doubled their advantage after 27 minutes when Vernon took full advantage of a defensive mistake by Caley debutant Roman Golobart to drive the ball past Ryan Esson .
Inverness pulled a goal back with 11 minutes remaining when Richie Foran seized upon Youl Mawene's careless header to fire past David Gonzalez.
Aberdeen made two changes to the side that was defeated 3-0 by Hearts at Tynecastle last weekend with Magennis and Ryan Jack both handed starts, defender Rory McArdle and striker Darren Mackie making way.
Inverness went into the match without seven players - including Ross Tokely who failed to overturn the red card he received in last weekend's 2-0 loss against Rangers.
Manager Terry Butcher handed a debut to new loan signing Golobart, while there were also starts for Andrew Shinnie, Nick Ross and Gavin Morrison.
Welshman Owain Tudor Jones missed out after undergoing knee surgery, while Gregory Tade and Aaron Doran dropped to the bench.
The Dons could have broken the deadlock after six minutes when Kari Arnason sent a tantalising cross into the box but Vernon failed to keep his header under the bar from only six yards out.
The opening goal for Aberdeen arrived after 12 minutes when Magennis showed great strength to ease past two defenders before slotting the ball across goal for Milsom, who turned the ball home.
The hosts may have had a long wait for their first strike of the season but they did not have to wait long for their second as Vernon pounced on a mistake from Golobart to run through on goal and coolly fire past Esson.
Aberdeen were looking full of confidence and energy and could have had a third when Magennis linked up with Fraser Fyvie, but the Northern Irishman's powerful effort whistled past the post.
Inverness thought they had pulled a goal back after 36 minutes when Jonny Hayes found the back of the net but referee Crawford Allan had already blown his whistle for an earlier infringement.
The Dons could have extended their lead before the break when Milsom's curling free-kick evaded everyone, but it bounced back off the post.
Inverness made the better start to the second half and Golobart could have made amends for his earlier error but the Spaniard failed to connect with Greg Tansey's inviting delivery.
The visitors made an early switch with Doran replacing the ineffective Shinnie after 53 minutes.
Aberdeen goalkeeper Gonzalez had enjoyed a relatively quiet afternoon but the Colombian was alert to gather the ball at the feet of Foran after an intelligent pass by Hayes.
The hosts were still looking dangerous on the counter-attack with Esson called upon to make a terrific save to deny Iceland international Arnason.
Aberdeen had a penalty appeal waved away after 73 minutes when substitute Mitch Megginson, who had replaced Magennis, fell under pressure from Chris Hogg.
Chris Clark was given his Dons debut in his second spell at the club when he came on for Fyvie with 15 minutes remaining.
A defensive lapse by Aberdeen gifted the Highlanders a way back into the match when Mawene carelessly headed the ball into the path of Caley skipper Foran, who had the easiest of tasks to pass the ball into the net after 79 minutes.
Foran then had a great chance to earn his side a point when he raced through on goal, but Gonzalez made a smart stop to ensure the Dons collected all three points.