The Russians were hoping for a repeat of last season's 2-1 victory at the Nou Camp but came up short against a team that had already made sure of the top spot in Group D and contained only two of their regular starting 11.
Rubin will have to make do with a place in the Europa League after finishing third in the group.
FC Copenhagen beat Panathinaikos 3-1 in the Danish capital to finish second and secure a place in December 17's draw for the knockout round.
Fans hoping for a show from Barca's three Ballon d'Or nominees, Lionel Messi, Andres Iniesta and Xavi, were initially disappointed, with Messi and Iniesta left on the bench and Xavi watching from the stands.
Coach Pep Guardiola had also rested striker David Villa, forward Pedro, captain Carles Puyol and first-choice goalkeeper Victor Valdes but the youngsters promoted in their place still had far too much quality for a toothless Rubin.
The visitors mustered only five attempts on goal to Barca's 17, while the Catalans enjoyed 75 percent of possession and showed they have plenty of in-house talent pushing for a regular place in the first team.
Defender Fontas struck in the 51st minute when his left-foot shot was deflected into the net off Vitaly Kaleshin and forward Vazquez, who had replaced the injured Jeffren in the 13th minute, added a second with a fine curled effort in the 83rd.
TRADEMARK RUNS
"It's impossible to be happier, scoring in the Champions League is the best," Fontas, who was making his first start in Europe's elite club competition, said in a television interview.
"Before the match I was a bit nervous but once I got out there everything changed," the 21-year-old added.
"Playing in this team makes everything easier and now I just need to keep working."
Messi's introduction with just under half an hour to go lifted the crowd and the reigning World Player of the Year managed some trademark weaving runs, although he failed to add to his six goals in the campaign.
The Argentina forward this week joined Iniesta and Xavi on the shortlist for the Ballon d'Or, to be announced later this month, the first time since AC Milan in 1989 that the same club provided all three finalists for the award.
Guardiola congratulated the B team players and singled out Vazquez, 23, who came through the club's youth academy at the same time as Messi, Arsenal captain Cesc Fabregas and Spain defender Gerard Pique, for special praise.
"He hasn't made it yet due to injuries, not because he lacks quality," Guardiola, himself a product of the Barca youth system, said at a news conference.
"He knows that he has to put in a good year in the second division to see what we will we do with him."
Barca's victory was slightly soured by the injury to Jeffren, who damaged a leg muscle, and a knock on the head to Bojan Krkic, who also had to be replaced in the first half.
The La Liga champions finished the group phase with 14 points from six matches, with Copenhagen on 10, Rubin on six and Panathinaikos on two.
