Souleymane Doukara put United in front early on but after bossing much of the match Leeds were forced into some late desperate defending.
Wanderers captain Darren Pratley netted for a fourth time in six games to pull a goal back before top scorer Gary Madine hit the post four minutes from time.
That proved as close as the Lancastrians got much to the delight of nearly 7,000 Leeds fans inside the storm lashed Macron Stadium.
And for all their late endeavours Wanderers struggled to build on a rare Championship victory over Milton Keynes Dons a week earlier.
Doukara shot the visitors in front after nine minutes with a large helping hand from at fault Wanderers keeper Ben Amos.
And fellow Frenchman Diagouraga netted his first goal since moving from Griffin Park six minutes from half-time to double Leeds’ advantage.
In fact, it was Diagouraga’s first since finding the net for Brentford in March 2013.
After beating Eastleigh in a third round replay and MK Dons last weekend more was expected of a Bolton outfit lining up with only one recognised striker in Madine.
The sides drew 1-1 at the Macron Stadium last October with Mirco Antenucci’s penalty cancelling out one of two goals by Shola Ameobi during his three-month stay with the Trotters.
Ameobi offered to play for free after his deal expired last Saturday. But the Trotters’ financial problems, including a £2.2 debt to the tax man, meant they had to refuse the former Newcastle man’s offer.
Impressive Diacouraga followed his goal with an early second half caution for bringing down Preston target Liam Feeney but Leeds remained on top.
Giuseppe Bellusci came forward from the back to take a free kick nearly 40 yards out that had Amos anxiously pushing the ball over the top of his crossbar.
Lennon tried to change Wanderers’ fortunes after 67 minutes taking off Arsenal loanee, Wellington Silva and Mark Davies for Kalyne Woolery and Jay Spearing.
Madine then shot shot straight at Marco Silvestri after 70 minutes in a rare home attack.
Scott Wootton joined the attack to fire high from a good position as Leeds sought a third goal to kill the tie.
Skipper Pratley, strangely subdued from recent displays, saw a goal bound effort blocked by Bellusci at the expense of a corner.
But the captain came up with his latest goal 10 minutes from time to give the Trotters’ hope. Madine then struck the woodwork with Leeds rattled.
Bolton’s cash flow problems eased before kick-off as the club announced a “second commercial transaction” with PBP Ltd.
In a statement the club said the agreement “provides much-needed short term funding, extends and progresses the long leasehold interests and joint venture development concept over the Macron Stadium North Car Parks that the parties had first entered into last year.
“PBP and the club now intend to bring forward detailed development proposals later in the spring, although the whole project is expected to take a number of years.
“The club had previously been in advanced discussions with Middlebrook Business Park Limited, but ultimately a deal could not be concluded.”