Spaniard Idiakez netted a superb free kick on the half hour mark and promising teenager Barnes completed the scoring with just a few minutes remaining on the clock.
Bolton had the best chances of the opening 25 minutes as Ricardo Vaz-Te and Gary Speed went close to breaking the deadlock. Vaz-Te failed to connect to a Kevin Nolan cross on 16 minutes and later saw his effort come off the woodwork whilst Speed could not get enough power on his downward header to trouble the Rams keeper Lee Camp.
New Derby striker Steve Howard then had a chance to open his account for his new club but his volley was to sail wide of the post of Wanderers custodian Jussi Jaaskelainen.
The opening goal came on 30 minutes when the Rams won a free kick just outside the area. Idiakez then went on to show many why he is one of the best dead ball specialists in the lower leagues when he planted an effort well out of the reach of Jaaskelainen.
Wanderers defender Nicky Hunt then had to leave the play a few minutes before the break through injury and was replaced by a player announced on the tannoy as Alex Perez.
After the half time interval Derby could have, and should have increased their lead but giant Danish defender Morten Bisgaard was unable to capitalise after Jaaskelainen spilled a shot by England youth player Barnes.
Both sides then made a number of substitutions as Jarek Fojut and Nathan Wolfe came on for the Trotters in place of Quinton Fortune and Stelios Giannakopoulos whilst Derby introduced Richard Jackson and the much travelled Canadian front man Paul Peschisolido for Paul Boertien and Bisgaard.
With 26 minutes left on the clock Jaaskelainen spared Bolton's blushes by saving smartly from pacy striker Tommy Smith. The former Watford and Sunderland attacker looked likely to score before the Finn denied him well from close range.
Barnes made sure that the Rams faithful went home happy though as the clock ticked down for full time. Bolton's substitute goalkeeper Ali Al-Habsi failed to hold onto the initial 86th minute shot by the much coveted youngster and he wasn't to be denied for a second time as he beat the Oman international from close range.
Bolton Wanderers: Jussi Jaaskelainen (Ali Al-Habsi), Nicky Hunt (Alex Perez), Quinton Fortune (Jarostaw Fojut), Kevin Nolan (Robert Sissons), Tal Ben Haim (Mark Charlesworth), Gary Speed, Stelios Giannakopoulos (Nathan Wolfe), Ivan Campo, Ricardo Vaz-Te, El-Hadji Diouf (Blazej Augustyn), Mark Ellis
Subs Not Used: Idan Tal, Chris Howarth
Derby County: Lee Camp, Marc Edworthy (James Meredith), Darren Moore, Michael Johnson (Lewin Nyatanga), Paul Boertien (Richard Jackson), Inigo Idiakez (Paul Thirlwell), Adam Bolder, Morten Bisgaard (Paul Peschisolido), Giles Barnes, Tommy Smith, Steve Howard (Lee Holmes)
Subs Not Used: Lee Grant
Attendance: 9,135
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