Uche Ikpeazu impressed for Cambridge in the opening 45 minutes and gave his side a deserved lead a little over a quarter of the way into the game, but the U's saw their levels drop as they missed out on a fixture with either AFC Wimbledon or Sutton United in the next round.
Cambridge produced an assured first-half performance that belied the 51 places separating the two teams in the English pyramid, but it was Leeds who so nearly opened the scoring three minutes in when a Marcus Antonsson cross caught Will Norris off guard and dropped onto his crossbar.
Leeds made eight changes to their starting lineup for this game, with manager Garry Monk clearly prioritising Friday night's huge league encounter with fellow promotion chasers Derby County, though the Whites will be without key man Pontus Jansson for that one as he was shown a 10th booking of the season here 23 minutes in.
Monk had bigger issues on his mind, however, as Ikpeazu gave the U's the breakthrough when using his power to work some space and beating a wrong-footed Silvestri at his near post.
Cambridge were really beginning to enjoy themselves, looking confident on the ball through the likes of goalscorer Ikpeazu and midfielder Luke Berry, who scored all four goals in the 4-0 rout of Coventry City in the last round.
The League Two side very much had another scalp in their sight, yet Leeds did end the first half on top with two attempts on target late on - Mowatt being denied by a fine Norris stop, before the U's keeper blocked Liam Cooper's header with his legs from the resulting corner.
Having collected 19 points from the last 21 on offer in the league, Cambridge were continuing to look lively early in the second half but failed to make their spell of possession count and were soon pegged back.
Mowatt was proving to be the visitors' most impressive performer and his cross from the byline into a dangerous position was attacked well by Dallas, who headed back across goal into the bottom corner for his first of the season.
Momentum swung as a result of that goal, with Antonsson testing an increasingly busier Norris down to his left and Mowatt then putting the Yorkshire outfit in front when helping on a powerful Jansson header from close range.
Cambridge were struggling to match their intensity levels of the first half as the final quarter of the game arrived, with chances at either end of the field drying up.
Ikpeazu did glance wide from a corner in the closing stages as Cambridge gave all they had, while Silvestri was lucky that nobody could capitalise when only parrying a Greg Taylor shot into a dangerous area, but Leeds did enough to see things through.