Brown grabbed the only goal of the game against the Czechs to hand the Scots their first friendly win at Hampden Park since victory over Australia back in 1996.
This match may not have been pretty to watch at times but handed the nation a much-needed boost ahead of the forthcoming European Championship qualifiers, where Scotland will again meet Michal Bilek's men.
Levein was forced to head into the match without the services of the talismanic James McFadden, who failed a late fitness test after struggling with a groin strain.
The Birmingham midfielder had been named in the starting line-up for the friendly but was replaced by West Brom's Graham Dorrans earlier on Wednesday.
Dundee United defender Andy Webster earned his first cap for four years, partnering Gary Caldwell at centre-half, while Kenny Miller led the attack.
Boyd - who refused to be considered for selection while George Burley was in charge and who had not pulled on the dark blue jersey for 18 months - started on the bench.
The Czechs carved out the first chance when Tomas Necid's pass was collected by Jaroslav Plasil but he drilled low past Craig Gordon's right-hand post from distance.
Scotland found themselves under pressure again when Lee Wallace fouled Ondrej Kusnir a few yards in front of the corner flag. Michael Kadlec delivered the free-kick into the packed box and it was Plasil who connected and nodded just over.
While Miller was looking isolated on his own up front, the Czechs continued to look dangerous and Tomas Rosicky's free-kick was flicked on by Necid for Vaclav Sverkos at the back post but he connected awkwardly and stabbed wide.
The best chance of the game so far came when Darren Fletcher lost possession to Rosicky and he set up the shot for Sverkos just inside the box but Gordon came to the rescue for the Scots with a fine save to keep the scoreline level.
Rosicky's corner then sparked a goalmouth scramble but Dorrans was able to hook off the line before anyone could bundle into the back of the net.
The crowd finally sparked into life when Barry Robson whipped a great ball in from the left for Miller but Tomas Sivok intercepted and nodded clear for a corner before the striker could connect with the header in front of goal.
The home side were then handed a free-kick on the edge of the area on the stroke of half-time after a handball from Sivok but Robson's curling free-kick was punched to safety by goalkeeper Jaroslav Drobny.
Czech Republic started the second half strongly and could have taken the lead when Rosicky's cutback found Sverkos and he unleashed a powerful shot that a full-stretch Gordon did well to tip just over the crossbar.
Scotland should then have been behind when Kusnir picked out Mario Holek in front of goal but he failed to connect well enough for the shot and the ball just escaped the out-stretched foot of Necid at the back post.
The first booking of the game came after an hour when Sivok was cautioned by the French referee for a crunching tackle on Brown.
However, the Celtic skipper recovered to fire Scotland into an unlikely lead just two minutes later. Wallace's cross from the left found Robson and he nodded into the path of Brown to rifle a left-foot shot past Drobny.
Boyd was then introduced to the action in place of Rangers team-mate Miller, with a mixture of cheers and jeers greeting his arrival.
Boyd tried to have an immediate impact on the game when he threw himself in front of a Fletcher cross but his header was well wide of target and did little to trouble Drobny.
Substitute Rudi Skacel tried to haul the Czechs back into the game with an audacious attempt from 30 yards but former Hearts team-mate Gordon was able to smother comfortably.
Boyd had an effort ruled offside and Steven Whittaker was denied by a great save as Scotland held on to begin their new era with a win.