Both sides spurned plenty of good openings, before the former Dagenham winger struck decisively in the closing seconds.
Nicky Bailey headed over after five minutes for the visitors and Matt Tubbs fired wide following a scramble from a corner.
George Porter missed two good chances for the hosts in the closing stages of the first half, firing over Blair Turgott's pass and missing the target from David Martin's cross.
Adam Cunnington fired wide from Turgott's cross, and winger Turgott was then denied by Ross Worner.
Alan Julian made a good save at the other end and Bradley Goldberg missed a great chance late on as he fired wide.
The game appeared destined for a draw until Dennis struck in injury time.
Report supplied by the Press Association.
Match ends, Bromley 1, Sutton United 0.
Second Half ends, Bromley 1, Sutton United 0.
Goal!  Bromley 1, Sutton United 0. Louis Dennis (Bromley).
Adam Cunnington (Bromley) is shown the yellow card for a bad foul.
Nicky Bailey (Sutton United) is shown the yellow card for a bad foul.
Substitution, Sutton United. Maxime Biamou replaces Bradley Hudson-Odoi.
Substitution, Sutton United. Dan Fitchett replaces Matt Tubbs.
Substitution, Bromley. Bradley Goldberg replaces George Porter.
Substitution, Sutton United. Gomis replaces Craig Dundas.
Simon Downer (Sutton United) is shown the yellow card for a bad foul.
Substitution, Bromley. Louis Dennis replaces Dave Martin.
Connor Dymond (Bromley) is shown the yellow card for a bad foul.
Second Half begins Bromley 0, Sutton United 0.
First Half ends, Bromley 0, Sutton United 0.
Craig Dundas (Sutton United) is shown the yellow card for a bad foul.
First Half begins.
Lineups are announced and players are warming up.
Louis Dennis fired a stoppage-time winner as Bromley beat Sutton United 1-0 in the National League.