The Serb saw off the 2014 US Open champion 6-4, 3-6, 6-3 to book another match against Federer, with the pair having met 45 times previously.
The Romanian rallied from a break down in the first set, as Barty won three of the first four games.
Play was briefly interrupted due to rain.
Djokovic broke Raonic's serve twice in a row to close the first set before he had his serve broken in what was otherwise a back-and-forth second set.
Stan Wawrinka took positives from his quarter-final loss against Roger Federer in Cincinnati. He'll face Milos Raonic later Friday.
The Dutch clay-court specialist ended Halep's streak of nine straight wins, including the title at Montreal a week earlier.
His record in OH is mixed, having won all five previous semi-finals, he has gone on to lose all five finals that he has reached, three of those against Federer whom he could line up against on Sunday evening. For the two men are very evenly matched despite different approaches to the game.
"It's been a hard week with rain delays and all that was happening". Halep has never won a Cincinnati title, losing the final match past year to Garbine Muguruza.
Wawrinka beat Marton Fucsovics of Hungary 6-4 6-3 in their third-round match.
Robert Mueller recommends prison sentence for ex-Trump aide George Papadopoulos
The diplomat passed along the information to USA officials, setting the investigation into motion. Now, Mueller has recommended that Papadopoulos see some time in prison.
Former champion Cilic made his way to the semi-finals with a 7-6 (5) 3-6 6-4 third-round win over Russia's Karen Khachanov before toppling Spaniard Pablo Carreno Busta 7-6 (7) 6-4.
Fourth seed Del Potro overcame Australian Nick Kyrgios 7-6 (4) 6-7 (6) 6-2.
The Croatian won his only Masters title in Cincinnati and having missed the event a year ago his run this week meant he was riding a nine-game winning streak.
"That's why I'm here", he said.
Today she'll try again against Dutch outsider Kiki Bertens, who will be playing her third final of the season after wearing down a tiring Petra Kvitova 3-6, 6-4, 6-2.
On the women's side, the top-ranked Halep beat Ashleigh Barty 7-5, 6-4 early Friday afternoon to reach the quarterfinals, then returned and knocked off Lesia Tsurenko 6-4, 6-1, raising both arms in triumph at the end of her long day featuring two full matches.
In the women's bracket, Madison Keys used her forehand to beat Angelique Kerber - one of her toughest matchups - and advance to the quarterfinals in-between the storms.
"I think it's the first time I'm going to have to be someone defending, getting to the finals of a Slam", she said.
"I had a match (point), so I was there", Halep said.
Goffin did not face a break point in defeating sixth seed Kevin Anderson of South Africa 6-2 6-4 in 76 minutes.