"It was such a shock, I did not expect to catch her, Maeve's a strong rider and I thought we'd be pretty even, so when I looked up and saw her there I thought 'wow'," Botha told Sky Sport.
"I honestly cannot believe it. Coming into this race I just wanted to get a PB and a 1.5 second PB is pretty big so I'm stoked with that."
Gate also set a Games record in qualifying for the men's 4000m individual pursuit, beating the record that Sexton had set 20 minutes earlier as Kiwis dominated at the velodrome.
The pair were guaranteed to take gold and silver, with the only question left being which Kiwi would take top spot on the podium.
Sexton flew out of the blocks in an attempt to blow Gate away, leading by 1.581 seconds after the first 1000m, but Gate held the gap steady at 1.444 seconds at the halfway stage, and then rapidly hauled in his teammate.
The gap evaporated by the time the pair reached the 2750m mark, and from there the result was never in doubt, with Gate cruising to a win by 4.419 seconds, finishing 0.6 seconds outside his Games record time.
The pair already had a bronze medal in their collection, after being part of the team pursuit squad that finished third yesterday, while Botha's gold came just 24 hours after she won silver as a member of the women's team pursuit.
Andrews also added another medal to her rapidly burgeoning haul, with a brilliant sprint victory.
A year after being beaten by Mitchell by 0.005 seconds in the 1/8 round at the Olympics in Tokyo, Andrews took her revenge, dethroning the Olympic champion with two powerful rides.
Mitchell was the top qualifier and had not lost a race all event, but Andrews came from behind on both occasions to overpower the Canadian and storm past on the line.
The first race was incredibly tight – just 0.003 seconds in it as Andrews won the photo finish - but there was no doubt about her second victory as the 22-year-old produced another highlight in an already brilliant career.
In the men's keirin, Callum Saunders finished fifth in the final, while Sam Webster (seventh) and Sam Dakin (10th) could only make the classification final.