Higgo, winner of the Gran Canaria Lopesan Open a fortnight ago, finished the third round with four straight birdies at Golf Costa Adeje.
The late burst saw him sign for a 64 and a 20-under-par total, meaning he is now a combined 61-under for 11 rounds in a three-event Canary Islands Swing.
The 21-year-old leads by two shots from Richard Mansell after the Englishman also signed for a seven-under effort, with Hill (66) one further back in third spot.
“I think someone is going to have to go very low tomorrow to win and, in order for me to win, I’ll need a bit of help from Garrick,” admitted Hill.
The 26-year-old Scot, a three-time winner on the Challenge Tour, started the day alongside compatriots Connor Syme and Richie Ramsay.
After both having to settle for par-71s, Syme and Ramsay slipped eight shots off the lead, but Hill is still right in the thick of things.
He birdied all five of the par-5s, completing the set at the last, where he had to lay up from close to the bottom of a tree but then controlled his wedge shot brilliantly to a tight front pin position before rolling in a curling 15-footer.
“It was important to stay patient as the pin positions were in difficult spots and I’m sure they’ll be tricky again tomorrow,” added Hill.
Securing that top-tour breakthrough on Sunday will see the Gleneagles Hotel-attached player in the US PGA Championship at Kiawah Island the week after next through breaking into the world’s top 100.
“The US PGA Championship has been the goal for the past three events, “ admitted Hill of his bid to join Bob MacIntyre and Martin Laird in the field for the season’s second major.
“Unfortunately, I’ve not put myself in a position to qualify until this week, so it’s going to require a good round tomorrow. That’s the only goal in mind at the moment.”
Higgo, who made two eagles earlier in the round before producing his strong sign off, booked his spot at Kiawah Island after breaking into the top 70 on the back of his Gran Canaria win.
Dean Burmester then made it back-to-back wins for South Africans when he won the Tenerife Open last weekend and now Higgo is on course to make that a hat-trick.
“It’s great to see the Scots going well,” said Hill of the efforts of a four-strong Calednian contingent this week, with Grant Forrest sitting just outside the top 30 on 10-under.
“It seems like we are trying to keep up with the South Africans. When you get a group of guys all pushing one another on it helps spur you on.”
That group also includes Craig Howie, who sits in a tie for 11th heading into the final round of the Dimension Data Pro Am, the third event of the new Challenge Tour season, at Fancourt in South Africa.
The 26-year-old Peebles player signed for an eagle and four birdies as he carded a five-under 67 to lie on 10-under, five behind leaders Chase Hannah from the US and home player Jaco Ahlers.