Monday's terrorist attack in the city, in which 22 people were killed by a suicide bomber at the Manchester Arena following a concert by American singer Ariana Grande, has cast a shadow over Manchester and the UK as a whole this week.
Friday's action was preceded by a minute's silence in memory of the victims and the competitors wore ribbons in solidarity.
Albert Square had hosted a vigil on Tuesday following the attack, but just three days later it served as the backdrop as Rutherford produced a season's best mark of 8.18 metres to win comfortably ahead of Emiliano Lasa of Uruguay.
Speaking on BBC Sport after his win, the London 2012 Olympic champion told the crowd: "It's been absolutely amazing to get you all out here in support of us. It's been an incredibly difficult week for everybody and I'm so pleased we can come here and give you something to smile about and enjoy.
"Manchester is one of my favourite cities in the world to go to. I love it for the football and I love it for all you guys getting behind us in sport. It truly is a special place."
Bradshaw, from Preston, smashed her own British record as she dominated the pole vault competition. Having sat back and watched compatriots Rachel Gibbons and Sally Peake, as well as Belgium's Chloe Henry, clear four metres but no more, Bradshaw entered the competition at 4.50m and went clear at the third attempt.
She then set a new national record of 4.72m before extending that to 4.80m and said: "They were great conditions. Once I got in the zone, to jump 4.72 and then 4.80 I am really chuffed."
Jonnie Peacock won the men's T44 100m in a time of 10.92 seconds while fellow Briton Sophie Kamlish took the notable scalp of Holland's Marlou van Rhijn to win the equivalent women's event.
James Dasaolu won the men's 100m while Asha Philip took the women's race ahead of Australia's Sally Pearson, who bounced back to win her specialist event the 100m hurdles.
In two rarely-contested events, American Johnny Dutch won the 200m hurdles while Lykourgos-Stefanos Tsakonas of Greece edged out British pair Harry Aikines-Aryeetey and Richard Kilty in the 150m.
