Tournament favourites Barca had been held to a slender 1-0 advantage from the first leg in the Italian capital last week.
But last season’s runners-up stormed into a 3-0 lead before half-time in front of 55,000 at the Camp Nou.
Swedish international Fridolina Rolfo struck twice in the first half either side of Mapi Leon’s spectacular long-range effort.
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 percent of their games in the Spanish league and only suffered one defeat all season, against Bayern in the group phase.
Barca 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.
