Inter Milan and Ajax Amsterdam secured tense victories, while 10-men Valencia held firm at Highbury to earn a 0-0 draw against Arsenal on a cold, wet night of Champions League action.
Group B remains tight with Valencia probably finishing the happier of the two sides after a scrappy game at a freezing Highbury.
The Spaniards, losing finalists in 2000 and 2001, were without injured captain and goalkeeper Santiago Canizares but his replacement Andres Palop proved more than adequate.
The Valencia keeper denied in-form striker Thierry Henry in the first half and produced even better stops to keep out a Freddie Ljungberg shot and a header by Dennis Bergkamp in the second period.
Valencia had to play the last 17 minutes with 10-men after Miguel Angel Angulo needlessly lashed out at Pascal Cygan to earn a red card, but either side could have snatched victory with efforts cleared off the line in stoppage time.
Arsenal stay top of the group with four points, the same tally as Ajax, with Valencia on two.
Roma suffered a second damaging defeat after their 3-1 loss to Arsenal when Ajax proved too good for them in frosty Amsterdam despite a batch of injuries and suspensions.
Swedish striker Zlatan Ibrahimovic gave Ajax a flying start with an 11th-minute goal after Roma goalkeeper Francesco Antonioli fumbled a simple shot.
The Dutch side, the last of whose four European Cup wins came in 1995, made it two through Finnish substitute Jari Litmanen after 66 minutes.
Argentine striker Gabriel Batistuta ensured a nervy finish with an 89th-minute header for Roma, but they face an uphill task having lost both their opening encounters.
In Group A Inter survived a late scare against Bayer Leverkusen to hang on for a 3-2 win at the San Siro and take command of Group A and Ajax were 2-1 winners over AS Roma in Amsterdam, lifting them level with Arsenal on four points at the top of Group B.
Rain in Spain denied Barcelona the chance to make history as their clash with Newcastle United was postponed until Wednesday after a downpour before kick-off swamped the Nou Camp.
Inter can enjoy the break before the resumption of the Champions League second phase in February but they were made to sweat by Leverkusen on a poor San Siro pitch.
Luigi Di Biagio, with a deft header and a thumping volley, put Inter two goals to the good within 27 minutes.
A half-volley by Boris Zivkovic just past the hour halved the deficit for the Germans, losing finalists last season.
But Inter seemed to have made sure when Leverkusen goalkeeper Jorg Butt diverted a cross into his own net under pressure from striker Hernan Crespo with 10 minutes left.
Leverkusen were not finished, though. Francoalda Franca made it 3-2 in the final minute and the visitors would have grabbed a point if Bernd Schneider's effort had not been ruled out for handball.
Barcelona's bid to equal AC Milan's Champions League record of 10 straight wins by beating Newcastle will have to wait for 24 hours, so Inter top Group A with six points out of six.
Barcelona have three points with Leverkusen in real trouble on zero points, the same as Newcastle.
Group A
Inter Milan 3 Bayer Leverkusen 2
Scorers:
Inter Milan: Luigi Di Biagio 15, 27, Jorg Butt 80og
Bayer Leverkusen: Boris Zivkovic 62, Francoaldo Franca 90
Attendance: 36,342
Group B
Ajax Amsterdam 2 AS Roma 1
Scorers:
Ajax Amsterdam: Zlatan Ibrahimovic 11, Jari Litmanen 66
AS Roma: Gabriel Batistuta 89
Attendance: 51,342
Arsenal 0 Valencia 0
Red Card: Miguel Angel Angulo (Valencia) 72
Attendance: 34,793