Care did extend his side's lead when he hacked on a loose ball and then collected 15m from the line.
Gloucester finally responded when Walker and Mike Tindall combined to put full-back Olly Morgan away in the corner, but Quins had the last word in the half as Malone kicked a penalty for an eight-point half-time lead.
The second half saw a more focused Gloucester cut the gap with a Walker penalty and 35m drop-goal, and Skinner's yellow card gave the fly-half the chance to put his side ahead for the first time.
Gloucester capitalised on their one-man advantage with replacement scrum-half Rory Lawson and Luke Narraway putting Strokosch away for a 40m sprint to the line.
Malone's clever angled run saw him cut back inside to score and give his side hope but Barkley slotted a penalty - having seen a previous effort miss the target - to seal the points.
Harlequins director of rugby Dean Richards:
"When you come in at half-time and their head coach is lambasting the referee and when you go out in the second half and you lose the penalty count 8-0 it begs the question 'what is going on?'
"It cost us last year and I would imagine that it cost a lot of people when they come down to Kingsholm because in the second half the referee would bottle it.
"I know [referee] Rob [Denby] and I like Rob as a person. I think that he is a more than capable referee, but this is a very difficult environment to referee in and when you get undue pressure like that then it makes it more difficult."
Gloucester head coach Dean Ryan:
"I didn't have a go at the referee. I think the interpretation of the ruck has been vastly different over the previous weeks.
"I asked him for clarity over the ruck law, I asked if people should be on their feet who clearly weren't.
"We've been contesting ball quite successfully for two weeks and suddenly we don't get one penalty to the attacking side or one turn-over so I asked him for clarity of his interpretation."
Referee Rob Denby: "As I walked to my dressing room at half-time both coaches politely came up to me. When they do that I am not going to just put my fingers in my ears."
Gloucester: Morgan; Watkins, Tindall, Barkley, Vainikolo; Walker, Cooper; Wood, Azam, Nieto, James, Brown, Strokosch, Hazell, Narraway. Replacements: Lamb for Walker (63), R. Lawson for Cooper (53), Dickinson for Nieto (14), Titterrell for James (68), Bortolami for Brown (63), Buxton for Hazell (53).
Not Used: Foster.
Harlequins: Brown; Strettle, Tiesi, Turner-Hall, Monye; Malone, Care; Jones, Fuga, Ross, Kohn, Robson, Robshaw, Skinner, Easter. Replacements: J Evans for Care (30), Botha for Fuga (56), Lambert for Kohn (56), Guest for Robshaw (56).
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