The hosts were always edging a tight contest even before promising scrum-half Spencer crossed for the opening score - and held firm after Tomas O'Leary's try had put the Wolfhounds back in it.
The Saxons began strongly, and Spencer capitalised on some solid forward work when he threw the dummy from the base of a ruck to cruise over unopposed in the 10th minute.
Wolfhounds wing Simon Zebo, who scored a hat-trick for Munster in Heineken Cup action last weekend, seemed certain to reply only to be denied by a powerful tackle from Matt Banahan, but the visitors did cross for a try in the 22nd minute.
David Kearney was the scorer, picking a lethal running line to carve through the Saxons midfield and race over from 10 metres out, cutting the hosts' half-time lead to 10-5 in the process.
Freddy Burns missed the chance to extend the advantage early in the second period, but 14 minutes in Waldrom collected a ricochet from a grubber-kick to barge over the try-line.
The try was a fitting reward for the Leicester No.8, who impressed throughout, in control at the base of a dominant England scrum.
In the loose he played as if he had a point to prove after being overtaken in the England pecking order by Ben Morgan and Luke Narraway since his role as an unused member of the World Cup squad.
Replacement O'Leary cut the deficit with an opportunist finish four minutes later, taking advantage of some sloppy tackling, but Burns kept calm to land two late penalties that rendered Zebo's last-gasp try a mere consolation.