Britain looked to be heading for victory after Welsh veteran Craig Bellamy, at 33 one of their over-age players, lashed home after 20 minutes.
But Senegal, who rallied strongly after the break, equalised in the 82nd minute when Moussa Konate timed his run perfectly to stay onside and clip the ball past goalkeeper Jack Butland.
Britain almost stole all three points in the 88th minute when Aaron Ramsey set up substitute Marvin Sordell but he shot against the bar.
The men's football competition is contested by under-23 teams who are allowed to field three players over that age, but Britain has been absent since the Rome Games of 1960 because of political differences involving Wales, Scotland and Northern Ireland regarding their own independence within FIFA.
But all that was forgotten as a near capacity crowd of 72,476 enjoyed a memorable night which began with Uruguay beating the United Arab Emirates 2-1 in the group opener.
They were also close to witnessing a British win, but were denied the chance despite an excellent performance from Britain's other Welsh veteran, skipper Ryan Giggs.
At 38 years and eight months old, and playing on his home Manchester United ground, Giggs became the oldest outfield football player ever to appear in the Olympic finals.
Giggs also had a hand in Bellamy's goal as the Senegal defence failed to clear his free-kick. The ball fell to Bellamy who scored with a fierce volley into the ground that flew up past goalkeeper Ousmane Mane.
Britain, playing only their second match together since the Olympics squad was announced, seemed far more settled from the start than they were at any time during last week's warm-up against Brazil in Middlesbrough which they lost 2-0.
However, they lacked bite in the second half and that was always inviting danger against Senegal, who qualified for their first Olympics after beating Oman 2-0 in a playoff at Coventry in April and had certainly not come to make up the numbers.
Senegal's tall, physically strong and hard-running side - typified by captain Mohamed Diame who has just moved from Wigan Athletic to West Ham United in the Premier League - deserved a point from a well-contested game.
But they also wasted a golden chance to equalise soon after Bellamy's goal when Sadio Mane dinked the ball wide after Butland made a rare mistake and hit a weak clearance straight to him.
Britain next face the United Arab Emirates while Uruguay play Senegal in another double-header at Wembley on Sunday.
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