The strapping Hampshire fast bowler troubled New Zealand's top order, exploiting the steep bounce at pace on offer on his home wicket.
His robust performance was made the more significant with the attendance of England selector James Whitaker, who will also have noted Hoggard's lack of penetration with the new ball.
Opening partner Graham Onions gave the Lions the ideal start to day two, trapping Jamie How lbw with his second delivery.
The ineffectual Hoggard was soon replaced by Tremlett, who immediately repaid captain Rob Key's faith with two wickets, dismissing James Marshall (10) and the dangerous Ross Taylor (5), leaving the tourists reeling at 47-3.
But Redmond and McCullum - leading New Zealand in Daniel Vettori's absence - steadied the innings, with the stand-in captain in particularly impressive form.
McCullum's 47-ball innings was curtailed seven runs short of a deserved 50 when he stalled running for a quick single, with Michael Carberry's direct hit catching him out of his ground.
However, the dismissal strengthened Redmond's resolve as he reached half century, as well as surviving a rap to the helmet from a hostile Tremlett bouncer.
England should have dismissed him three runs short of his century, but Graeme Swann grassed a regulation catch at second slip off Onions.
And Redmond compounded Swann's error by passing his previous best first-class score of 135 to put New Zealand on course for a first innings lead.
"I wanted to bat through the whole day and to do that is quite an achievement
so I'm pretty pleased with that.
"I copped a few but that's all part and parcel of being an opener. Every now
and then you're going to get one that goes past your face but the good thing was
they continued to bowl like that so it was good practice," Redmond said afterwards.
The second new ball offered more assistance to Hoggard, who had to wait until the 85th over for his first wicket of the day when Jeetan Patel edged to second slip.
The Yorkshireman dismissed Tim Southee and Iain O'Brien in quick succession, leaving Chris Martin at the crease at stumps.