Bojan was a late replacement for Sweden striker Zlatan Ibrahimovic who injured his calf in the warm-up but was not missed as a weakened Barca swept aside Bilbao.
Jeffren, 22, opened the scoring after 27 minutes and Bojan, 19, a fellow product of the club's youth system, struck either side of half time to put the European champions in control.
Lionel Messi netted his 26th league goal of the campaign in the 67th minute and although Markel Susaeta pulled one back for the visitors, the result at the Nou Camp was never in doubt.
"I suppose you were shaken when you read the team sheet," Barca coach Pep Guardiola joked to reporters. "But it is possible to go to the end of the world with these players."
Sevilla ended a run of eight games without a win by beating lowly Tenerife 3-0 in the late match.
Frederic Kanoute set new coach Antonio Alvarez on course for his first victory after 22 minutes and Luis Fabiano doubled the lead, chesting down and swivelling to score a superb second just before the break.
Jose Carlos curled in a free-kick near the end to leave Sevilla fourth on 48 points.
Real Zaragoza pulled away from the relegation zone with a 2-0 home win over Malaga thanks to goals from Leonardo Ponzio and Humberto Suazo.
CHAMPIONS LEAGUE
Guardiola had Tuesday's Champions League quarter-final return leg against Arsenal and a top-of-the-table La Liga clash at Real Madrid next Saturday on his mind when he put out an unfamiliar side at the Nou Camp.
He was forced to replace Ibrahimovic but chose to include rarely used Dmytro Chygrynskiy at centre back while left back Maxwell started in midfield.
With Xavi, Pedro and Seydou Keita on the bench and Daniel Alves suspended, Barca lacked their usual fluency.
Jeffren stroked the ball in at the back post from Eric Abidal's low cross and it was Carles Puyol's interception and pass that set up Bojan for the second before the break.
Bojan struck a fierce third from the edge of the area after a sweeping move in the 59th minute before Messi slid in Pedro's cross to secure victory.
Barca may have failed to reproduce the thrilling football that illuminated their 2-2 draw at Arsenal in the week but a lacklustre Bilbao offered little until a breakaway goal sparked a late flurry.
The victory came at a cost to Barca though. Injured Ibrahimovic was ruled out of the Arsenal game and is a doubt for the trip to the Bernabeu, as is defender Gerard Pique who has pulled a thigh muscle.
