Swiatek came from a set down to beat Jasmine Paolini in her singles rubber but the Italian earned immediate revenge over the five-time Grand Slam winner in the deciding doubles clash.
Paolini and veteran Sara Errani overcame Swiatek and Katarzyna Kawa 7-5, 7-5 to send the four-time champions through to Wednesday's final.
Great Britain face Slovakia in the second semi-final on Tuesday.
In the opening singles rubber, Italy's Lucia Bronzetti beat Magda Linette 6-4, 7-6 (7/3).
That was followed by Swiatek's battle with Paolini, which ran over two-and-a-half hours and saw the Pole win 3-6, 6-4, 6-4.
"It was tough today... the intensity was insane, I was a little bit tired but I said to myself, you still have to play the doubles, you have to give everything for Italy, for my team," said Paolini.
"When I lost the (singles) match I was a little bit sad, but then tried to go in the locker room and think positive about the doubles."
Poland were in the semi-finals for the first time but came undone just when it seemed they had done enough for a tie-break, losing the last six games of the final set in the doubles.
"Honestly I don't think I've ever been so tired," said Swiatek.
Linette, the world number 38, was largely outclassed by Bronzetti, ranked 78th, in the first singles rubber.
At 4-1 down in the second set, Linette battled back strongly to force a tie-break but was eventually beaten when she slapped a return into the net after saving one match point.
It left the pressure on Swiatek to deliver, which she did in thrilling fashion.
Beaten every time in their three prior clashes and having never managed to take a set off Swiatek, Paolini battled with fierce determination from the outset.
Swiatek crushed the world number four in straight sets in the French Open final earlier this year but found a vastly tougher opponent in Malaga.
The Pole saved two break points to hold at 2-2 and then broke with a fizzing forehand to take the lead.
It did not deter Paolini, who doubled down and won the next four games, securing two breaks of her own, to claim the first set.
Swiatek spurned three break points in the final game and showed signs of tiredness after helping Poland reach the semi-finals by winning both her singles match and a doubles rubber against the Czech Republic.
Paolini had done the same for last year's runners-up Italy against Japan but dug deep to keep Swiatek at bay until the 10th and final game of the second set, which the Pole won to force a third.
After the players exchanged breaks in the decider, Swiatek eventually triumphed when Paolini went long.
Swiatek won 13 of the 16 break points she faced, proving the stronger in the key moments.
"For sure it was tough, my energy level was down in the second set but I managed to get back and that was the most important thing," said Swiatek, explaining she had "no time to celebrate" as the job was not done yet.
'Found the way'
In the first set of the doubles decider, the teams stayed on serve until Italy's combination of Errani and Paolini broke for a 6-5 lead and then held to claim the set.
Swiatek and Kawa responded strongly, opening up a 5-1 lead in the second set before suffering a collapse.
The relentless Italians fought back in stunning fashion by winning six games straight, sealing the victory when Swiatek overhit a forehand.
"It was not easy, it was a really long day, I didn't start the doubles that well... but then I found the way, I think we played a really good match," said Errani.
The 37-year-old served for the last point of the match underarm, a habitual move of hers.
"I did it many times this year, (when there's) tension it's a good combination sometimes to do it," she added.
