Edmund, 22, won 6-3 3-6 6-2 in a rain-delayed match to set up a last-eight tie against top-seeded Milos Raonic.
The Canadian beat Croatia's Borna Coric 6-3 7-6 (7-2) in Florida.
At the Rio Open, Britain's Jamie Murray and doubles partner Bruno Soares beat Marcus Daniell and Marcelo Demonliner 6-4 6-2 to reach the semi-finals.
They will face Argentines Andres Molteni and Diego Schwartzman next.
Meanwhile, British number four Aljaz Bedene lost 7-5 7-5 in the second round of the Open 13 in Marseille to Frenchman Lucas Pouille.

It was the final major barrier to building an additional 20,000 homes in the city over the next decade.
The Local Development Plan (LDP) sets out where new houses can be built, based on a forecast that the population will grow by a quarter over 20 years.
Cardiff council said the city was in "dire need" of the plan, to help it manage its growth.
A final decision will be made by the local authority in the coming weeks, but it is expected to be rubber stamped by the council.
Under the plan:
The inspector has not given as much protection to the greenbelt on the edge of the city as a number of councillors and residents had campaigned for.
The process has been long and controversial.
Supporters say the expansion is needed to deal with the shortage of housing in the city, while opponents claim the city's infrastructure will not be able to cope.
The plan is based on projections of a growth in the population from the 320,000 to nearly 400,000 over the period between 2006 and 2026.
The last time Cardiff grew at this scale was at the height of the coal industry a century ago.
Cardiff council cabinet member for planning and sustainability Ramesh Patel said the city was "in dire need" of the plan.
"The last plan was approved 19 years ago and has led to insufficient land being made available for urgent housing needs," he said.
"When the new plan is finally adopted at the end of January, we will ensure that developments in the city are managed effectively with new transport infrastructure, schools, health facilities and other community facilities.
"The plan gives us the control to guide development and manage the growth of the city."

The pair from Haverhill have won the UK's second biggest ever lottery prize after being the only winners in Friday's lottery draw.
Camelot said the pair would reveal their plans for the future on Tuesday at Down Hall Country House Hotel in Hertfordshire.
The lottery organisers said the total prize money won by the couple was £148,656,000.
Camelot said the lucky ticket holders would be revealed at the hotel in Hatfield Heath, near Bishop's Stortford, at 11:30 BST.
A National Lottery spokeswoman said: "We are looking forward to welcoming the ticket-holder into our millionaires club, joining the 2,900 millionaires created by the National Lottery to date".
The ticket is the second biggest National Lottery win behind Colin and Chris Weir from Ayrshire, who scooped £161m in July 2011.
It is also the second winning ticket by a couple from East Anglia in less than a year after Dave and Angela Dawes, of Wisbech, Cambridgeshire, won £101m in October.
The winning numbers were 11, 17, 21, 48 and 50. The lucky stars were 9 and 10.
It is the seventh Euromillions jackpot to be won in the UK so far in 2012.
In Friday's draw another UK millionaire was created in the Millionaire Raffle Selection game, with the winning code JDW 016965.
Camelot said to date Euromillions players have raised £28bn for National Lottery Good Causes.
Watch live coverage of the winning couple's TV interview on the BBC News website at 1130
British number three Kyle Edmund progressed to the Delray Beach Open quarter-finals with victory over Taiwan's Lu Yen-hsun on Thursday.
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A controversial plan for the biggest expansion of Cardiff in a century has been approved by a planning inspector.
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A couple from Suffolk have won £148m on the Euromillions lottery.