The visitors inflicted most of the damage in the first half, punishing Kildare for their wastefulness and pouncing for two goals from Califf and Barry Flanagan to lead by 2-5 to 0-5 at half-time, despite having played into the strong wind and heavy rain.
They controlled proceedings well in the second half and it took Kildare 25 minutes to record their first score of the second half, a point from Eddie Heavey.
Both sides produced some good football in the opening period.
Heavey might have had a goal from the very first attack and Rob Kelly had a shot splendidly saved by Craig Lynch.
Instead, it was Louth who found the net, as Califf produced a wonderful finish off the inside of the upright for a 10th minute goal.
Flanagan pounced 15 minutes later after full-back Luke Flynn failed to deal with a difficult high ball, and with Califf adding four points — including a superbly-struck 45 into the wind — Colin Kelly’s charges were in control.
While Mikey Conway scored one spectacular point from play, Kildare were reliant on three points from Ray Cahill frees to remain in touch and they offered little threat after the resumption.
Louth pulled clear in the second half thanks to four more points from Califf, who finished with a tally of 1-8 and were worthy victors.
Both teams finished with 14 men after Eoin Powderly and Ronan Holdcroft were shown red cards following an off-the-ball altercation.
J Califf 1-8 (0-4fs, 0-1 45); B Flanagan 1-0; R Holdcroft 0-2(1f); J McEneaney 0-1 Kildare: R Cahill 0-4(fs); M Conway, E Callaghan, E Heavey, C McNally 0-1 each
C Lynch, P Rath, D Finn, K Toner, D Maguire, E Lafferty, K McLoughlin, J Califf, T Durnin, D Byrne, C McKeever, Cathal Bellew, A Reid, B Flanagan, R Holdcroft. Subs: J McEneaney for Flanagan BC (43), G McSorley for McLoughlin (48), D McMahon for Bellew (55), M Rafferty for McKeever (67), Ciaran Bellew for Maguire (68)
C Heeney, E Powderly, L Flynn, O Lyons, S McNally, E Bolton, K Murnaghan, Daryl Flynn, M Byrne, P O’Neill, M Conway, E Heavey, E Callaghan, R Kelly, R Cahill.
Daniel Flynn for Daniel Flynn BC (29), R Houlihan for Murnaghan (46), C McNally for O’Neill (46), É O’Connor for Conway (50), P Kelly for L Flynn (55), F Dowling for Callaghan (57)