Luis Suarez gave Barca a 21st-minute lead but Roma equalised eight minutes later with a wonder goal from defender Alessandro Florenzi.
Florenzi drilled a right-footed shot from just over the halfway line and the ball cannoned into the back of the net off a post.
Barca had plenty of chances to move back in front and were unlucky not to do so in the 78th minute when Lionel Messi, making his 100th Champions League appearance, saw his left-footed shot from the right side of the area hit the crossbar.
Roma held on for a point to deny their former coach Luis Enrique a perfect start to the competition.
Barca started brightly and sent an early warning when Messi got past his marker and drilled a left-footed effort over the bar.
A long spell of possession from the visitors ended with a Messi shot that went over the bar. In the 18th minute, Daniele De Rossi made a vital block from Messi’s goal-bound attempt as Barca got closer. Three minutes later and the visitors moved in front.
Suarez headed home Ivan Rakitic’s cross towards the far post to beat Roma goalkeeper Wojciech Szczesny.
Barca demanded a penalty in the 24th minute when Suarez went down in the area following contact from Szczesny. However, the referee waved play on.
Roma pulled level soon after thanks to a brilliant long-range effort from Florenzi that gave visiting goalkeeper Marc-Andre Ter Stegen no chance.
Barca reacted well and began to exert control as Messi saw several long-range attempts go over the bar.
The Argentinian continued to terrorise the Roma defence and in the 38th minute, Messi got past his marker and struck a low shot from 12 yards that was only just kept out by Szczesny.
Messi picked up where he left off after the re-start, but he was once again thwarted by Szczesny as his fine effort from the edge of the area was saved.
Roma’s hopes looked to be dwindling when Rudi Garcia was forced to make his first substitution six minutes after the break, with Szczensy forced off and Morgan De Sanctis replacing him.
Barca surged forward and in the 76th minute Neymar came close to scoring but saw his goal-bound shot blocked.
With seconds remaining, Jordi Alba fed Neymar in the box and his effort was blocked by Manolas as Roma held on for a valuable point.
Thomas Muller’s scoring hot-streak continued as he netted a brace to steer Bayern Munich to a 3-0 win at Olympiacos in their Champions League Group F opener.
Muller put the Bayern ahead in the 52nd minute with a lofted effort from outside the box which looked as if it had been intended as a cross.
Substitute Mario Gotze then lashed into the net with a minute of normal time remaining, before Muller converted a penalty in stoppage time to take his tally for the season to eight Bayern goals and 11 overall, including those scored for Germany.
Hakan Calhanoglu scored a brace either side of Javier Hernandez’s first goal for Bayer Leverkusen as the German side made a winning start in Champions League Group E by seeing off BATE Borisov 4-1 at home.
Leverkusen took the lead in the fourth minute through a delightful Admir Mehmedi effort, only for their Belarusian opponents to draw level nine minutes later via Nemanja Milunovic’s deflected header.
An even bigger deflection saw the hosts go back in front two minutes into the second half when Calhanoglu’s shot diverted in off Dzyanis Palyakow.
Hernandez, signed last month from Manchester United, then wrapped things up in the 59th minute, marking his first Leverkusen start with a tidy right-footed finish, before Calhanoglu converted a 75th-minute penalty.
Dynamo Kiev substitute Vitaliy Buyalskyi struck a late equaliser to rescue a point for his side as their opening Champions League Group G clash against Porto ended 2-2 at the Olympic Stadium.
Midfielder Buyalskyi, a second-half replacement for Oleh Gusev, ran onto a mis-hit shot in the 89th minute to fire home and deny the Portuguese victory after Vincent Aboubakar’s double had cancelled out Gusev’s opener for the Russians.
Group E Bayer Leverkusen 4 BATE Borisov 1; Roma 1 Barcelona 1.
Group F Olympiakos 0 Bayern Munich 3.
Group G Dynamo Kyiv 2 Porto 2
Group H Gent 1 Lyon 1; Valencia 2 Zenit St Petersburg 3.
QPR 2 Blackburn 2.