Olazabal, who has re-designed some of the holes at Pula, fired a 5-under 65 in round two.
France's Gregory Havret carded a 4-under 66 on Friday and is alone in third place at minus-5.
Broadhurst, who won this year's Open de Portugal, parred his first two holes, then ran off three birdies in a row from the third to move up the leaderboard. He birdied seven, but dropped his first shot of the tournament at the par-4 eighth.
The Englishman parred No. 9, but caught fire after the turn. He drained a 10-foot birdie putt at 10, then spun his approach back to 2 feet to set up an easy birdie putt at the 11th. Broadhurst collected his third birdie in a row from the rough at 12 when his 7-footer fell into the cup.
Things turned badly quickly for Broadhurst. His drive on 14 landed in the right rough, then his approach fell into the water on the left. He walked off the hole with a double bogey and fell back to 7 under par for the championship.
He still held the lead, but his four-shot advantage shrunk, thanks in part to Olazabal's ascension up the leaderboard. Broadhurst had to scramble for par at 16 when his second sailed over the putting surface. He converted the par save and holed a 6-footer at the 17th to stay at minus-7.
Broadhurst parred the par-3 18th to take the 36-hole lead.
'I'm quite happy with 7 under,' admitted Broadhurst, who is 28th on the European Order of Merit. 'I feel reasonably comfortable out there. My short game is pretty good, the concern is getting it on the fairway and on the green.'
Broadhurst has a lot going for him this week. He has posted back-to-back top-10 finishes in this event and the win in Portugal in April has the 40- year-old feeling confident.
'It certainly helps,' acknowledged Broadhurst. 'I know I've been there and handled it pretty well. We've seen in the previous two tournaments that anything can happen down the straight. The last nine holes, you can span a few out.'
Olazabal made the turn at 2 under par and got into second place early on his second nine. He sank a 15-footer for birdie at the 11th and collected his second in a row from 9 feet out at 12.
The Spaniard saved par from 7 feet at 14 after having some problems with a cart path. Olazabal missed a 25-foot birdie putt at 15, but converted from 12 feet out at No. 16. That birdie got him to 6 under par and one back.
He parred the final two holes to put himself into position for his first European Tour title since the Hong Kong Open three years ago.
'If I hit the ball the way I did today, I will be pleased with that whatever the outcome,' said Olazabal. 'It's important to win, but it will come if I keep on playing good.'
Mattias Eliasson (68), Simon Khan (69), Jose-Filipe Lima (68) and Wade Ormsby (66) are knotted in fourth place at 4-under-par 136.
Jose Manuel Lara shot a round of 1-under 69 and is tied for eighth place with Miles Tunnicliff, who posted a 2-under 68. The pair is knotted at 3-under-par 137.
Defending champion Sergio Garcia and two-time winner on the 2005 European Tour schedule, Miguel Angel Jimenez are part of a group tied for 10th place at minus-2.
First-round leader Jonathan Lomas struggled to a 4-over-par 74 and is tied for 21st place at minus-1.
The 36-hole cut fell at 4-over-par 144 and 80 players made it to the weekend.