Djokovic, the top seed and defending champion, advanced by beating fifth-seeded Jo-Wilfried Tsonga of France 7-5, 6-1. Federer, seeded third, breezed past Andreas Seppi of Italy 6-1, 6-2.
In the other semifinal, No. 2 seed and five-time champion Rafael Nadal of Spain will meet sixth-seeded countryman David Ferrer (live at 7 a.m. PDT on Tennis Channel).
Federer, 30, leads the series against Djokovic 14-10 (3-1 on clay). But Djokovic, who will turn 25 on Tuesday, has won four of the last five encounters.
It will be the first meeting between the pair since Djokovic's epic 67 (7), 46, 63, 62, 75 victory in the semifinals of last year's U.S. Open. Federer held two match points for the second consecutive year against Djokovic in the semis at Flushing Meadows and lost each time.
Djokovic also won the Italian Open in 2008. Federer is 0-2 in finals at the Foro Italico, falling to Felix Mantilla of Spain in 2003 and Nadal in 2006 (7-6 in the fifth set).
In Friday's doubles quarterfinals, unseeded Lukasz Kubot of Poland and Janko Tipsarevic of Serbia ousted No. 2 seeds and former Stanford All-Americans Bob and Mike Bryan 6-4, 6-4. The Bryan twins won the tournament in 2008 and 2010.
NCAA Championships in Athens, Ga. -- No. 11 Stanford defeated No. 6 Kentucky 4-1 in the round of 16 at the NCAA Championships, but No. 14 Cal lost to No. 2 Virginia 4-0.
John Morrissey clinched the match for the Cardinal at No. 4 singles when Tom Jomby was defaulted on match point for hitting a ball at the chair umpire with Morrissey leading 6-1, 3-6, 5-4. Jomby had been assessed a point and game penalty earlier in the match.
At No. 1 singles, 36th-ranked Bradley Klahn of Stanford routed third-ranked Eric Quigley 6-1, 6-2. Klahn won the 2010 NCAA singles title in Athens as a sophomore.
Stanford (20-8) will face Virginia (27-1), last year's runner-up, Sunday in the quarterfinals. Cal finished 14-12.
See below for full results of Friday's Stanford and Cal matches.
Men's Challenger in Fergana, Uzbekistan -- Second-seeded Raven Klaasen and Izak Van der Merwe, both of South Africa, outplayed third-seeded John Paul Fruttero, a former Cal All-American living in San Jose, and Uladzimir Ignatik of Belarus 6-4, 7-6 (2) in the doubles semifinals of the $35,000 Fergana Challenger. Fruttero and Klaasen have played together for most of 2011 and this year.
Men's Futures in Tampa, Fla. -- Christian Harrison, the 17-year-old brother of rising young American Ryan Harrison, beat Pedro Zerbini, an ex-Cal star, 6-4, 6-1 in the quarterfinals of the $10,000 Tampa USTA Men's Pro Circuit Futures.
USTA National Seniors in La Jolla -- Top-seeded Ros (Fairbank) Nideffer of Rancho Bernardo defeated third-seeded Tracy Houk of Half Moon Bay 6-1, 6-3 to win the 50s singles title at the USTA National Senior Women's Hard Court Tennis Championships.
Nideffer, a 51-year-old South Africa native, reached the Wimbledon quarterfinals in 1988 and 1989, and won the French Open doubles title with South African Tanya Harford in 1981 and American Candy Reynolds in 1983.
In the 60s semifinals on Thursday, second-seeded Mary Ginnard of Fort Lauderdale, Fla., outlasted third-seeded Martha Downing of Shingle Springs 3-6, 6-4, 6-3.
2. Klahn/Morrissey (STAN) vs. No. 38 Musialek/Rossi (KENT) abandoned.
3. Gomez/Jomby (KENT) d. Kandath/Stineman (STAN) 8-2.
Order of finish: 3, 1.
2. No. 29 Ryan Thacher (STAN) d. No. 15 Alex Musialek (KENT) 6-1, 7-5.
3. Matt Kandath (STAN) vs. No. 22 Anthony Rossi (KENT) abandoned.
4. John Morrissey (STAN) d. No. 80 Tom Jomby (KENT) 6-1, 3-6, 5-4 (default).
5. Daniel Ho (STAN) d. No. 111 Alejandro Gomez (KENT) 6-3, 2-6, 6-4.
6. Robert Stineman (STAN) vs. Grant Roberts (KENT) abandoned.
Order of finish: 1, 2, 5, 4.
2. J. Uriguen/Shane (UVA) vs. No. 66 Cueto/B. McLachlan (CAL) DNF.
3. Domijan/Frank (UVA) def. Bayane/Scholnick (CAL) 8-3.
Order of finish: 3, 1* (Virginia wins doubles point)
2. No. 39 Alex Domijan (UVA) def. No. 58 Nick Andrews (CAL, Folsom); 6-1, 6-3.
3. No. 2 Mitchell Frank (UVA) def. No. 70 Carlos Cueto (CAL); 6-4, 6-4.
4. Drew Courtney (UVA) vs. Christoffer Konigsfeldt (CAL); 6-2, 4-6, 2-3 DNF.
5. No. 82 Justin Shane (UVA) def. Gregory Bayane (CAL); 6-1, 6-3.
6. Julen Uriguen (UVA) vs. Riki McLachlan (CAL); 7-6(7), 2-0 DNF.
Order of finish: 2, 5, 3*
Sunday -- Rome (women), final, Tennis Channel, 4:30-7 a.m. (live), 9:30-11:30 a.m. (repeat), 2-4 p.m. (repeat), 6:30-8:30 p.m. (repeat). Rome (men), final, Tennis Channel, 7-9:30 a.m. (live), 11:30 a.m.-2 p.m. (repeat), 4-6:30 p.m. (repeat), 8:30-11 p.m. (repeat).
Sunday -- NCAA Division I Team Championships, men's quarterfinals, Athens, Ga. No. 11 Stanford vs. No. 2 Virginia, 2 p.m. (PDT).
Monday -- NCAA Division I Team Championships, men's and women's semifinals, Athens, Ga.
May 22 -- NCAA Division I Team Championships, men's and women's finals, Athens, Ga.
May 23-28 -- NCAA Division I Singles and Doubles Championships, men and women, Athens, Ga.
May 27-June 3 -- $50,000 FSP Gold River Women's Challenger, Gold River Racquet Club, 2201 Gold Rush Drive, Gold River.
MAY 27-JUNE 10 -- FRENCH OPEN.
June 2-10 -- $15,000 Sacramento Men's Futures, Park Terrace Swim & Tennis Club, 5500 Parkfield Court, Sacramento.
June 9-10, 16-18 -- NorCal 18 Junior Sectional Championships, Sacramento State.
June 9-17 -- $15,000 Chico Men's Futures, Chico Racquet Club & Resort, 1629 Manzanita Ave.
JUNE 25-JULY 8 -- WIMBLEDON.
July 7-15 -- WTA, Bank of the West Classic, Stanford.
July 9 -- World TeamTennis, Sacramento Capitals' season opener at Boston, 4 p.m.
July 12 -- World TeamTennis, Capitals' home opener (with Mardy Fish) vs. Kansas City, Sunrise Marketplace Stadium, Sunrise Mall in Citrus Heights, 7:35 p.m.