Alesana Tuilagi followed Flood's conversion with another five points, allowing Flood to step up and convert his second of the afternoon.
The fly-halfs exchanged one more penalty apiece prior to the break to send Leicester in ahead at the half.
Flood scored his second try of the afternoon immediately after the restart, before then kicking a penalty a minute later to add to his side's total.
Substitute Stephen Myler kicked the extras to reduce the deficit to 16 points, but Flood's third penalty of the afternoon all but put the Tigers out of reach.
Chris Ashton added a late five points to the home team's total, but the visitors escaped with a comfortable win.