Spieth's bid to become only the sixth man in history to win the Masters and U.S. Open in the same year is on track after he carded a second-round 67, while Reed posted a 69 on Friday.
One shot back is overnight co-leader Dustin Johnson who stumbled late on to post a 71, with South African Branden Grace joining the American on four-under.
World number Rory McIlroy is nine shots off the pace at four-over, while a second-round 74 saw Phil Mickelson’s hopes of ending his U.S. Open drought severely dented.
There was more misery for Tiger Woods, with the 14-time major winner missing the cut by twelve shots after shooting a six-over 76 to amass the highest 36-hole total of his career.
Spieth, who made six birdies, one bogey and a double-bogey on the par-four 18th, is also on track to become the first player since Gene Sarazen to win multiple majors at the age of 21 or younger.
The world number two, who hit a first-round 67, began strongly after starting on the back nine, with birdies on the 10th, 14th, 15th and 17th before he faltered on the 18th after twice finding the sand.
He bounced back with a birdie on the first before slipping to a bogey on the seventh. He would soon pick up the lost stroke, birding the par-three ninth to finish at five-under.
Reed looked to set to take an outright lead into the weekend’s running, but a bogey at the 18th after a poor approach shot saw him drop back to the mark set by Spieth.
The 24-year-old’s round was nothing if not eventful, with only six pars featuring on a busy scorecard. After recording two early birdies, Reed stuttered around the turn, registering three bogeys in four holes. However, he recovered with a birdie at the 11th before producing an eagle-two at the par-four 12 after finding the green from the tee.
Two further bogeys followed, but a birdie at the 16th got Reed back on track. A great day would not end well though, with Reed three-putting at the last after giving himself a lot of work to do with a poor second shot.
Dustin Johnson, who finished in a tie for fourth at last year's U.S. Open, remains in contention to win his first major as he sits one stroke behind Spieth and Reed following a second-round 71.
Johnson sat atop the leaderboard for much of the day after consolidating on his strong opening round with three birdies and two bogeys on the front nine. The big-hitting American started the back nine with a birdie at the 11th, but three bogeys on the last five holes saw him drop off the pace.
Level with Johnson is South African Grace, who followed up a solid opening 69 with a 67 on Friday that included an eagle-three at the par-five eighth, four birdies and two bogeys.
Joost Luiten, Tony Finau, Daniel Summerhays and Ben Martin are a further shot back on three-under.
Jason Day joins J.B. Holmes and Jamie Lovemark on two-under, but there are concerns regarding whether the Australian will make the weekend after he collapsed on the ninth – his final hole of the day – after being hit by a case of vertigo.
Day was able to finish the holes after receiving treatment from paramedics, but having been plagued by ill-health all year it is unclear if he will be able to continue.
Henrik Stenson, who shared the overnight lead with Johnson, could only manage a 74 which sees him drop back to one-under and a share of 12th.
McIlroy was left a frustrated figure after he only just sneaked into the weekend's running after dropping three shots in his final two holes to fall back to four-over.
McIlroy eagled the par-four 12th to get to one over but then four-putted at 17th to fall to three over. A further bogey at the last saw him finish just above the cut line.
Tiger Woods' misery continued as he followed up his career-worst U.S. Open round of 80 with a bogey-filled 76.
Woods, playing the back nine first, began in ominous fashion when he pulled his second shot to the 10th onto a steep slope to the left of the fairway. So precarious was his position that he lost his balance and fell while attempting to take his stance.
The first of his three bogeys on the back nine was the result of that adventure, with a birdie at the 12th his lone bright spot. Matters got even worse on his closing nine though, with five bogeys – including three in a row from the seventh to ninth – permeated with a lone birdie.