Thiem, who lost to Nadal in the 2017 final, beat the Spaniard 6-4 6-4, also avenging his defeat in last year's French Open final.
Medvedev, 23, will now play the victor of the other semi-final between Rafael Nadal and Dominic Thiem on Sunday, after avenging his Brisbane International final defeat by Nishikori in January.
A sense of Déjà-vu in Barcelona: a week ago the Sand-opener in Monte Carlo Rafael passed Nadal in the semi-final.
Kerr calls Lillard's game-winner against Thunder a 'good shot'
Should they advance, they will face the victor of the Houston Rockets-Utah Jazz series in the second round. Kanter called it a blessing to be with the Trail Blazers, who won their first playoff series since 2016.
Notably, Nadal has also never lost a semi-final match in Barcelona and is heading for his record 12th title in this tournament this week. Nishikori had to survive a double break point to hold his next service game and stay in the match.
The 11-time Barcelona champion saved four of five break points and broke four times in what could have been his last meeting with Ferrer, who is retiring after the Madrid Open next month. The second set brought small-margin battle as well and it was Kei who fended off a break point in the first game to avoid an even bigger deficit, delivering four good holds after that and breaking Medvedev in game eight with a smash victor that pushed him 5-3 up.
"This match was important for me", Nadal said. "I played against a great opponent", Nadal said. "So when I started to miss the second serve, I really lost a little bit of the confidence on trying to go for a good first serve, because I was without confidence on the second, so that affects the first".
While 2018's beaten Roland Garros finalist looks to be building towards another challenge in Paris, the usually dominant Nadal has concerningly now failed to reach consecutive finals on his favoured surface. It was a close match that lasted 3 sets but Daniil Medvedev held his nerve to win the overall contest.
England's Alex Hales serving suspension for 'off-field incident'
He had already missed two games and the remainder of the ban was suspended for 12 months so he could be available for selection. England supporters want a nice, smooth approach to this World Cup but we know England cricket and it's unlikely to go that way.
Nadal had served for the opening set at 5-4, but was broken by the world No. 63.
"I enjoyed the match, I'm feeling the way I want to feel about my game".
"It was hard, I started well but the court was slower when the rain started coming down, that damaged me but I still played a competitive game". "And as I said before, I am happy and I am confident that I made a big improvement this week".
Winners & losers from Iranian oil sanctions
China now opposes the recent announcement made by the Trump administration on the sanctions imposed. That cooperation helped tighten the oil market, pushing oil prices up more than $70 a barrel.