Halep, who thanks to Caroline Wozniacki's loss to Kiki Bertens in the previous round will retain her world number one spot, had dominated Pliskova's twin sister Kristyna a day earlier to stretch her run in the Spanish capital to 15 matches.
The big-serving Canadian grabbed the first break of the match in the 11th game, and despite seeing Dimitrov fight back to force a decider, he closed out a 7-5, 3-6, 6-3 win.
The Russian former world number one has shown only flashes of the play that has earned her five grand slam titles since returning from a doping ban past year.
An honest Pliskova said she was eager to avoid facing Halep after their last meeting in the last eight of the Australian Open, which the Romanian won to improve her record to six wins and one defeat against the world number six. I mean, yeah, was some good matches, some up and down sometimes. She really was moving very well and also hitting the balls, the serve. But yesterday against Julia, I had to play a little bit better.
The two-time Grand Slam champion was in trouble when she dropped serve in the fifth game of the second set, but won 10 of the next 12 games to race to victory.
French seventh seed Caroline Garcia also reached the last four with a 6-2 6-3 win over Spain's Carla Suarez Navarro.
"It's always just one victor, so one of us will end the streak, but I'm already pretty satisfied with my performance on the clay: in Prague, here, in the Fed Cup", said Kvitova.
Shapovalov will next face world No. 22 Kyle Edmund of Britain, a 6-3, 6-3 victor over 10th-ranked David Goffin of Belgium.More news: Rooney agrees 'deal in principle' to move to MLS
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Women's singles top seed Simona Halep was among leading players to be beaten today at the Mutua Madrid Open in Caja Mágica.
Sharapova had overcome Kristina Mladenovic to reach the quarters, and carried that form with her into the opening set, taking it 6-4 with a crucial break in the 10th game. Djokovic, recently back from injury, is now under-ranked at 12th.
Canadian teenager Denis Shapovalov produced a relentless display of big-hitting to deny France's Benoit Paire the ideal 29th birthday present with a 7-6 (5), 4-6, 6-4, victory in the second round of the Madrid Open on Tuesday. Rafael Nadal lurks in the other half of the draw.
"I think much better".
After breaking twice to seal the first set, Edmund spurned one match point at 5-2 on Goffin's serve and then delivered a double fault a game later to set nerves jangling.
World No. 43 Shapovalov struck 38 winners, including 18 on his forehand, to seal victory in just over two hours.
Lajovic moved on to meet sixth-seeded Kevin Anderson, who eliminated Philipp Kohlschreiber 6-3, 7-6 (7).