The Six Nations champions had led 9-6 at the break thanks to three Leigh Halfpenny penalties, with Felipe Contepomi slotting a penalty and Nicolas Sanchez landing a drop goal for the Pumas.
Halfpenny extended Wales' lead with a fourth penalty early in the second half, but a penalty and drop goal from Sanchez, plus converted tries for wings Juan Imhoff and Gonzalo Camacho saw the visitors secure their second win over Wales in Cardiff, 11 years to the day after their first.
The defeat puts a major dent in Wales' hopes of securing a top-four place in the world rankings ahead of next month's 2015 World Cup draw, but they can have no qualms after being exposed by Argentina.
And there looks set to be further bad news for Howley with Jamie Roberts and Alun Wyn Jones picking up injuries that put their involvement in the rest of the autumn series in doubt.
The Pumas, for their part, look to have quickly learnt the lessons of facing the All Blacks, Australia and South Africa during their maiden Rugby Championship campaign, and a frustrated Howley acknowledged the visitors appear to have moved their game to a new level.
He said: "I am disappointed, frustrated and annoyed because we know we are a better side than that.
"We talked about it being an arm wrestle for 50 minutes and we were 12-6 ahead but we looked one-paced.
"When you play Argentina, tempo, pace and intensity are important but there is no doubt their experience and exposure to the Rugby Championship has taken that Argentina side to another level.
"They played the All Blacks, South Africa and Australia over a six-week period and they have certainly learned from that and we were exposed to it today [Saturday] and we very much came second."
Wales' chances were not helped when a clearly concussed Roberts was helped off after a clash of heads with Gonzalo Tiesi, while lock Jones was withdrawn with a shoulder problem just before the break.
Howley said: "Jamie has a bump on the head, it's a mild concussion to say the least. Alun Wyn has done his AC (joint) so we will have to wait on the medical opinion for that but it does not look good at this time and it will test our strength in depth and these next three games are very important."
Assistant coach Shaun Edwards pulled no punches in his assessment of the performance, and felt Wales had badly missed the injured trio of centre Jonathan Davies, prop Adam Jones and flanker Dan Lydiate, as well as Roberts after he went off.
He said: "I definitely thought the impact from the Argentina bench was better than ours. We went into the game with certain personnel missing and it showed quite dramatically in the last half hour.
"Both starting centres from the Grand Slam were missing, we had our number six and number three missing and it showed, and we have to get the other players up to pace as quickly as possible.
"But it was obvious there is a disparity at the moment between our first-choice XV and the players who have got those positions now."
Argentina coach Santiago Phelan agreed with Howley's view that his side's experience in the Rugby Championship played a big part in their victory, which tees them up perfectly for their remaining tour fixtures against France and Ireland.
He said: "We are very happy with our performance today [Saturday]. The team took the initiative in the first 20 minutes and played very well in the second half, moving the ball and keeping possession.
"The intensity of the game was very high, but the Argentinian players have had a good experience playing in the Rugby Championship and have learned to play at this intensity.
"Today [Saturday] was a good step forward for our team in terms of intensity and tempo and scoring points, which was one of our major goals for this game."