Fridolina Rolfo sent last season's runners-up ahead with a clinical finish after 11 minutes and Mapi Leon lashed a home a spectacular second from 30 yards out.
Swedish left-back Rolfo added a third just before half-time to extend Jonatan Giraldez's side's advantage on the Serie A leaders.
Asisat Oshoala netted from close range immediately after the break and Patri Guijarro headed home the fifth from a corner.
Annamaria Serturini pulled one back for Roma against a Barcelona side who have won 100 per cent of their games in Liga F and only suffered one defeat all season, against Bayern in the group phase.
The 2021 winners have now reached the semi-finals in five consecutive seasons and leading through Salma Paralluelo's strike at the Stadio Olimpico last week, were firm favourites to progress at home.
Barcelona set two world record attendances of over 91,000 each at Camp Nou last season en route to the final, where they were beaten by Lyon -- and will face either the French giants or Chelsea in the semis.
Almost 55,000 watched on Wednesday and saw Rolfo open the scoring with her 10th goal of the season across all competitions after Oshoala knocked the ball into her path.
The Nigerian striker missed two good chances herself to double Barcelona's lead before centre-back Leon took matters into her own hands with a vicious blast from distance which flew past Camelia Ceasar and into the net.
Back to her tricky best after a long injury absence, winger Caroline Graham Hansen dazzled at times and helped carve out the third with a tempting cross which Rolfo swept home from point-blank range.
Former Barcelona captain Vicky Losada had a bittersweet return with Roma, able to play at Camp Nou for the first time in her career but taken off at half-time by Alessandro Spugna.
Aitana Bonmati set up Oshoala for her fifth Champions League goal of the season, making her the joint second top scorer.
Guijarro, one of Barcelona's best players this season in the absence of the injured Ballon d'Or winner Alexia Putellas, nodded home the fifth, before Serturini's consolation for Roma.
Barça have now reached the semi-finals in five consecutive seasons and will face either defending champions Lyon or Chelsea in the last four.
"We can't hide that our aspirations are at the max," said Barcelona coach Jonatan Giraldez.
"Olympique (Lyon) and Chelsea are the best in Europe, it's a reality and it will be difficult, but it's true that playing the second leg at home gives us a feeling of strength."
Arsenal blow away Bayern
Arsenal overcame a 1-0 first-leg defeat to reach the last four for the first time in 10 years in front of a record crowd of over 20,000 for a Women's Champions League game in England.
Despite the absence of injured star forwards Vivianne Miedema and Beth Mead, the Gunners blew Bayern away in the first half.
Frida Maanum levelled the tie with a blistering strike in off the underside of the crossbar on 20 minutes.
Moments later Arsenal led as Stina Blackstenius had the simple task of rounding off a brilliant team move with a header into an unguarded goal from Katie McCabe's cross.
Only some wasteful finishing from Jonas Eidevall's side meant there was a nervy finale.
Leah Williamson and Caitlin Foord missed glorious chances to extend the lead, while Lotte Wubben-Moy hit the crossbar.
But Arsenal held out to extend Bayern's wait to win the competition.
Chelsea hold the upper hand ahead of Thursday's blockbuster quarter-final clash after the English champions won 1-0 away to Lyon in the first leg.
Wolfsburg also hold a 1-0 lead in the other quarter-final over Paris Saint-Germain ahead of the second leg in Germany.
