Britain’s heptathlon champion Katarina Johnson-Thompson ran the fastest 800m race of her life to take Olympic silver while the women’s 4x100m relay team missed out on gold by seven-hundredths of a second after a fumbled final handover.

An electrifying performance in the final 800m run in the seven-event discipline won a first medal at a Games for the 31-year-old double world champion and delivered a moment of joyous redemption after repeated Olympic disappointment.

It had followed relay sprints in which Britain’s women’s team pushed the US right to the finish line and the men took bronze in the 4x100m behind Canada and South Africa, after the American favourites mangled a handover.

It was, however, Johnson-Thompson, known as KJT, who had the spectators in the Stade de France on the edge of their seats as she tried to complete the 800m run in a time that was about eight seconds quicker than Nafissatou Thiam, the Belgian Olympic champion. In a moment of high drama Thiam at one point appeared to slip, but remained on her feet.

Straining every sinew, Johnson-Thompson came only a couple of seconds short of her target on a track made slick by early drizzle in Paris but it was still a performance to earn her a place alongside Jessica Ennis-Hill and Denise Lewis among the British Olympic heptathlon greats.

She said: “I can’t even describe the words but I’m just so relieved and so happy that I have an Olympic medal to add to my collection. It was the only one I didn’t have and it’s been so hard getting back to this point.”

Johnson-Thompson said her boyfriend, the retired hurdler Andrew Pozzi, had hinted at a celebratory meal. “My boyfriend has had a restaurant in mind and I think he’s planned a big meal,” she said. “One of the restaurant owners just called me over and said ‘that’s my restaurant, I’ll see you tomorrow’ so I think we’re in for a big feed.”

Earlier in the day, a teenager known as The Terminator claimed a shock Olympic gold for Britain in men’s sport climbing before Team GB’s sprinters teed up an exhilarating final night of athletics on Saturday.

Le Bourget climbing centre echoed with chants of the name of 19-year-old Toby Roberts as he clinched the “boulder and a lead” title in Paris after a slip by the favourite, Sorato Anraku of Japan.

Roberts, who was given the Arnold Schwarzenegger-inspired nickname courtesy of his determination on the wall, said: “I’m just absolutely lost for words. To find out that I got the gold in that moment, it was just truly incredible.”

The event had combined a round in which athletes negotiated four boulder “problems” on a 4.5-metre-high wall within a time limit, and a “lead” where they had to climb as high as possible in a single attempt.

“I’ve been training for this moment my whole life, and now I’ve just won,” said Roberts, from Elstead, Surrey.

Gold in the women’s Madison in the velodrome was taken by the Italian team of Chiara Consonni and Vittoria Guazzini but Team GB’s Elinor Barker and Neah Evans snatched a silver medal after winning a final double-points sprint. Jack Carlin, 27, from Paisley, took bronze in the men’s cycling sprint.

Johnson-Thompson, a two-time world champion, had been broken in Rio, according to her Olympic teammate Jessica Ennis-Hill, and traumatised by an injury-ravaged Tokyo Games. This was the race she had been working to but it was always set to be an uphill struggle for gold.

Johnson-Thompson’s personal best had until Friday night been just over six seconds faster at 2min 5.63sec, compared to Thiam’s 2 11.79. She needed a time difference of 8.9 seconds to realise her dreams. She delivered a new personal best of 2min 4.90 to Thiam’s 2min 10.62sec – a gap of just under six seconds.

It was time to add to her two world titles, two Commonwealth titles and a European silver, after a string of disappointing Games, coming 13th at her debut in 2012, sixth in 2016 and failing to finish in Tokyo. But the top podium would prove just out of reach.

She said: “I can’t complain. Nafi ran a PB and she’s probably the greatest of all time. I’m so blessed to be having these big rivalries with one of the best of all time and I ran a PB and that’s all I can ask of myself.”

The heroics in front of a raucous crowd followed a personal best by Max Burgin, who has been compared to a young Sebastian Coe or Steve Cram, as he led the way for Britain’s runners by qualifying for Saturday’s men’s 800m final in 1:43.50.

Burgin, 22, from Halifax, said he was benefiting from a lack of pressure going into what will be the biggest race of his life.

The Olympic 400m silver medalist Matt Hudson-Smith said he also believed he could snatch a second medal in Paris, after qualifying with Charlie Dobson, Sam Reardon and Toby Harries in the 4x400m team with a time that was second only to the US team.

Hudson-Smith, 29, from Wolverhampton, said: “I’m genuinely wired, it’s been an incredible two days but I’m finding another gear because we want to push for a medal. I want to push to be a double Olympic medallist. We can go win it. We’ve got the team, we got the mentality, we’ve got the coaching staff. Let’s make history. This team can do anything. We can get the British record, European record, and if we dig deep the world record.”

In the US team for the first time was the 16-year-old Quincy Wilson, 16, who became the youngest track-and-field Olympian after taking part in the heats.

“It was an amazing moment,” said Wilson. “I had my family – mom, dad, sister, grandma, her sisters and a lot of family – in the stands.”

The British women’s 4x400m team of Lina Nielsen, Jodie Williams, Hannah Kelly and Yemi Mary John reached the final in 3:24.72, raising hopes of a podium position. Nielsen, 28, from London, said: “We’re all in such good shape, I think there was no doubt that we rival for a top spot. Perhaps even challenge for first.”

In the final swimming event in the Seine, Hector Pardoe and Toby Robinson, who finished sixth and 14th in the men’s 10km marathon, said they hoped that London could be inspired to clean up the Thames. Robinson, 27, from Wolverhampton, said: “It would help inspire the next wave of young swimmers to take up open water.”